Social media & modern recommendation engines have made thinking other people's thoughts seductively easy. Modern apps give us an infinite feed of semi-engaging thoughts to consume in any media we want - from tiny text messages on Twitter to 30 hour audiobooks on Audible. Movies on netflix, short movies on youtube, not to mention podcasts and so on.
And no question, lots of it is fantastic content! Its just - all the things I'm most proud of doing have needed way more of my own thoughts than the thoughts of others. At least 10x as much time genuinely thinking and creating vs time spent in consumption mode. But with so much great content out there, I doubt many of us take the time to do enough thinking. I know I don't, and it chills me to the core.
So I'm not surprised that taking a walk - an activity during which its hard to consume the thoughts of others - leads to an increase in creativity. I would expect that anything which disconnects us from recommendation engines and notifications would be rehabilitating for our inner voices. And what is creativity but our inner voice given form in the world.
I've thought about this, but I thought it was my thought. Without the internet, I could have likely continued walking around thinking it was an original idea.
I think in order to make something yours, even if it's a thought others have had before, you take the whole of something, wrestle with it internally, then pull it apart and put it back together. There will inevitably be parts of the whole that you leave by the wayside, and other parts you stay with. Since you are a person with unique experiences, what remains - when combined with the viewpoints that come from those unique experiences - will effectively be yours.
Reflection time is hugely needed. But I don't know that it's hugely important to distinguish in that time between reflection on your "own" thoughts and those that originated in some way outside your head, because at some level it's impossible to make the distinction. You'll need a huge base of exposure to other people's ideas if you hope to assemble them into a new and interesting combination of your own.
Art history is riddled with such free-thinking products. To an extent punk is derived from the avant-garde movement.
Closer to home, there wouldn't be data science without statistics though you can find data scientists that don't necessarily grok statistics.
This is IMO one of the reasons we get so much cargo-cults and tribalism around software development overall. Too much detachment in the name of abstracting complexity away.
for the entirety of human history, we've been growing by collecting and synthesizing the wisdom of others that come before us: standing on the shoulders of giants. we are surprisingly incapable when working alone. for instance, there are numerous examples of eruopean explorers starving or dying of easily preventable causes in the Americas, in the very spaces where natives had been living for tens of thousands of years. they weren't stupid, they just didn't have the foresight, or cultural knowledge that the natives did. 
There's the idea that "everything is a remix" , popularized by Kirby Furguson. he essentially states that we don't have much (if any) original creative thought, and that most "creative" ideas are just remixes of other ideas. this goes back all the way to prehistory and especially applies to traditional myths passed down orally through generations: see the numerous flood myths prevelant in almost all societies.
what I'm getting at is that we are not inherently creative beings, we don't do especially well when coming up with completely novel ideas. what we ARE good at is learning, synthesizing, and remixing.
so I'm not entirely sure that our "moth to an interesting article" behavior online is really that bad for us, I think its more the state that we are in when we do that - skim, go 'oh that's neat' and move along.
 The Secret of Our Success by Joseph Henrich
I've drastically reduced my usage of social media services not for productivity reasons, but because I'm not comfortable with the insanely detailed profile I end up revealing.
For example: a real conversation has so much more depth because of facial expressions, change in voice, and so on. An emicon can't replace that.
Isn't it impossible to tell which thoughts are 'your own'? Not sure if that distinction even makes sense.
Once I walk a little and get out of the room it's like turning a new page. I see things a lot clearer because I don't feel distracted about all the tiny things that creep into my mind after a while of sitting down and concentrating on the same problem. They're not "in the cache" anymore, probably because they were the easiest to discard when walking through the door.
It's not always useful, this "walking out and then back in the room" takes the edge off of any witty comeback I may find (and oh they're good sometimes). :D
I just had to walk out of the room to remember this ^^ corner case.
I agree that staying in the same room seems to have a considerably lessened benefit (seems to reduce the benefit to almost zip). I have to leave the room, just getting up and standing about in a small space doesn't do it.
Any mundane activity can help with creativity, so long as it doesn't take very much brain power. Walking, showering, doing dishes, going for a drive, doing something repetitive. To a certain extent, taking a bus and other things that make you bored or otherwise give you time to think/daydream. I don't know where any of the research I've read is, but I honestly thought this was a known thing already and I'd be interested to see if walking has some sort of advantage over things like washing dishes or driving.
Combine this sort of thing with learning and improving your general world knowledge. Learn about things you didn't know about or aren't connected to your work. Learn about other people. Do things that challenge your world view. Other people's ideas often play into this so long as you give yourself time to think about things.
I personally think this is why people think drugs make them more creative: There are many drugs out there that can change your perspective on things, even if it is temporary and slight. Alcohol is enough. There more perspective on has and the more knowledge one has, the greater the base is for a person to be creative and combine ideas.
Then the participants walked on the treadmill, at an easy, self-selected pace that felt comfortable. The treadmill faced a blank wall. While walking, each student repeated the creativity tests, which required about eight minutes.
So, they re-did the tests they did shortly before and came up with more solutions?
That cannot be it. I hope this is sloppy reporting and the paper tells a different story. A story of a control group. Of some people walking first and sitting later and vice versa. And so on.
It seems they took your point into consideration. Check Experiment 2 section.
Seriously though, something happens out there, from my perspective subconsciousness talks to me, slips notes with various reminders that I utterly forgot for weeks, or makes connections to things I never thought about before. I think it is because its so natural to walk for us, our consciousness is completely free.
And on weed, alone (important part, if I am with somebody my focus is on communication and not some inner voices), this flow of thoughts and ideas becomes so intense that I usually have to stop and start typing them into some notepad in phone, otherwise they will be forgotten within minutes (the curse of short term memory effect of weed).
I've come up with at least 20 different startup ideas among other things, some entirely out of software engineering (my daily job). Some of them look a bit moonshot-ish in hindsight, some I found out somebody else already did without my prior knowledge (ie self-belaying device for climbing), some just look hard but doable.
IMO I can mention 2 correlated factors, Some of us are kinetic thinkers and we need the movement to accelerate the clock and effect more misfires causing "aha moments". And blood speed and pressure is a thing in our brains.
Personally, I have found myself in situations where a problem's solution is presented very clearly in the middle of a low pace run (7 mins per km) and immediately go back to my shelter with something new to try out.
It's not the only method I come up with ideas but it's a pretty reliable one.
For every day I use it, I'll probably look at it once a month. The process of writing it down helps cement and make you remember it better.
It helps to just have a notebook and pen+paper handy, and draw ideas there. Also helps to learn something your not good at like drawing or music
The process of logging ideas is important though. Doesn't matter where you log it. I have 100 first drafts in wordpress, I let those drafts compete with each other before fleshing one out once a week or every 2 weeks, depending on what mood im in
I build up so much crap at my office, mainly mental crap. After a couple hours of slack/code/etc i lose my focus and it helps to turn off everything and reset. "Ok , now what do i _really_ need to accomplish in the next two hours, for myself. Not for co-worker that needs help that I have been helping"
Apart from the 'reset', i do tend to think of different solutions for various problems that are floating about my brain while walking as well. Different data structures, process flows, refactors etc.