Being able to solve people's problems doesn't mean you need to be able to program.
What is a "real programmer", anyway? Is it knowing how a CPU works? Managing memory? If you rely on the garbage collector, do you really know what you're doing? If you write a Rails app without fully understanding HTTP, are you just plumbing?
Does it matter?
The reason we build tools and abstractions is to allow us to accomplish higher-level tasks without worrying about lower-level ones. Does it help if you understand lower level ones? Sure. But for millions of apps and websites that aren't Facebook or Hacker News or Firefox, the only problems are high level.
I think that it matters if you can dig into anything. Given reasonable timespan being able to learn x64 machine code, debug and fix buggy driver if necessary, for example. If you're program has GC issues, being able to read papers, read GC source code if necessary and find right set of parameters or change some lines of code. If your Rails app has vulnerability because of underlying HTTP issues, being able to learn more about those HTTP issues, read RFC if necessary, read Ruby http code if necessary and provide required fix. If your manager heard about Meltdown issue and wonders whether our services are vulnerable, real programmer should be able to read papers, understand vulnerability and whether it's important (to shut down services, for example) or not.
Abstractions are leaky. I've yet to encounter one which doesn't leak.
Though if you're working in a team, it's not necessary for everyone to be real programmer. One or two is enough. Those tasks which require real programming are rare, most of tasks are mundane.
Sure, I'll concede all of those points! But I think they fundamentally change the question, because now you're presenting a different set of problems to solve.
Understanding one level of abstraction doesn't mean that you understand the levels above or below it. It's perfectly possible (likely, even!) that a team will have someone who can build a good Rails app and someone else who can make sure the HTTP code and infrastructure is secure, yet those people won't have many skills that overlap.
Yes, there are definitely good programmers and bad programmers. IMO, that has to do with how effectively you can solve problems you care about, not (as the comment to which I was replying suggests) the level of abstraction you're comfortable with.
I'd say the world 'real' muddles things up and injects too much value judgment, and with little purpose I can see other than making oneself feel special (or inferior).
I'd much prefer 'highly skilled' or 'advanced', if at all necessary.
The XKCD is a bad example in this case, as it is mostly about domain specific knowledge of computational theory or standardized algorithmic approaches to the problem spaces presented within those domains, whereas "low-level" is something different ... primarily referring to common layers underlying many domains.
Most programmers never have to write low-level code.
This is a good thing.
It doesn't mean they can't, it just means we've moved on from wasting our time re-implementing solutions to problems already adequately solved for a general case. Finally.
Manual memory management is frankly insane outside of extreme edge cases today.
What is a "real programmer", anyway? Is it knowing how a CPU works? Managing memory? If you rely on the garbage collector, do you really know what you're doing? If you write a Rails app without fully understanding HTTP, are you just plumbing?
Does it matter?
The reason we build tools and abstractions is to allow us to accomplish higher-level tasks without worrying about lower-level ones. Does it help if you understand lower level ones? Sure. But for millions of apps and websites that aren't Facebook or Hacker News or Firefox, the only problems are high level.