Ideas are everything. Execution is everything. You get one wrong, you get everything wrong
That's pretty much my take on the whole "ideas vs execution" debate, with a nuanced caveat or two. Neither a good idea nor great execution is sufficient to build a great startup, and I'd argue that both are necessary depending on how you define "good idea".
bad idea, poorly executed: FAIL
bad idea, well executed: FAIL
good idea, poorly executed: FAIL
good idea, well executed: MAYBE
I say it depends a bit on how you define "good idea" though, because I strongly believe that a "good idea" does not (necessarily) need to be something earth-shattering, brand new, never-seen-before, etc. Sometimes your "good idea" can actually be something that already exists, and you plan to win by simply executing better than the competition.
All of that said, I agree very much with gweinberg on the point about ideas within the context of execution mattering. In fact, reading that just sparked a couple of actionable ideas on my part. Those are the articles I love reading on HN.. the ones where I walk away with a new TODO (other than "read this later").
In our community, "bad idea, well executed" is also a maybe - not a "fail" - on succeeding - as by definition if you're executing well you know when to pivot and aren't afraid to do so, or you are simply succeeding despite a bad idea, or are doing what it takes to push it through.
Also I'd like to point out that the definition of executing well is almost begging the question. To answer the question "Was it well-executed?", we apply the heuristic "Did they succeed? get numbers up? generate sales, investment, etc..". Then we are only 'testing' our own definition and every successful company will be "well-executed" and vice versa.
I'm not sure how to improve these definitions, but it's important to realize that asking how well a team is executing is problematic.
You would need a definition of "execution" that lets you point out teams that are executing well and failing, before you had a concept of 'executing well' that is useful and not just a proxy for 'succeeding.'
 Plenty of big, multibillion dollar product categories (McDonald's for one, two year mobile phone contracts for another), are a really bad idea. If either category didn't exist, I doubt an investor would think you could convince people to like it, on a national scale.
I'm not sure if it's "begging the question" so much as just over-generalizing. That is, I'm not sure there's an easy, binary distinction between "good idea" and "bad idea". It may be that ideas are on a continuum from "really bad" ---> "ok" ----> "really awesome" or whatever. And a slightly dodgy, but not great, idea may succeed if coupled with sufficiently awesome execution. OTOH, a kinda good idea, with dodgy execution, can fail out.
And, this is skipping the issue of refining the actual idea itself as you learn, which may not be quite as dramatic a shift as an actual "pivot".
Your point is definitely valid though, that there is a some semantic confusion around this whole discussion.
Of course it may be some kind of selection bias, but my impression from seeing many startups, is that:
with good execution, bad ideas often lead to good ideas. I know more than one nontrivial business that essentially started out with a bad idea, but the execution was enough to see what was bad about it, and that there's a related idea that's good.
I've seen much fewer cases where, despite bad execution, a good idea shines through: sooner or later, usually sooner, the competition wins when the execution is bad.
It's a false dichotomy as you say, and a big reason people claim "ideas don't matter" is because their definition of execution includes "getting a better idea" (or, pivoting). If the idea truly didn't matter then you should be able to succeed _with that same idea_. Semantics I guess, but it is a platitude that doesn't get questioned much, it seems.
The thing is good execution can make a mediocre idea into a success.
The reason we ascribe so much more to execution around here is because coming up with good ideas doesn't seem incredibly difficult. However it is one of those things that looks easy but isn't in reality.
Experience has taught me otherwise. The idea is part of the execution. Meaning that you cannot do well what you have not defined. Doing something requires knowing how and what you are doing. There are the same thing, and not different entities. The whole notion of idea versus execution is wrong. You cannot execute something which you have not thought of properly. Thus, the idea is bad, and the execution will be bad. You can, however, improve on the execution and end up with something entirely different. But it will also improve on the idea itself.
think of the test. What is being tested? If you haven't noticed, most software is paid for by advertising, or selling people's private information. The 'market' where a lot of software can survive is being tested on several criteria.
1. does it trick people into giving away as much info as possible?
2. does it make people Dependant on it?
3. does it provide any important social value to those who have lots of money?
Even in a market where people pay real money for software, typically either people need the software but won't buy it because it costs too much, or the software is so cheap that they sacrifice some of their needs.
The market is where good ideas go to die.
Let's have a thought experiment. Imagine a world where we can get our best and brightest people to work on any software for free. There is no need to pay them or the hardware they use.
Do you think society would dedicate their brightest people to working on advertising (Google, Facebook), or peddling cheap Chinese goods (Amazon), or locking businesses into perpetual software cages (Microsoft, Oracle, Apple).
Do you think the market could have created the Internet?
Do you think the market could have created PCs?
Do you think the market could have selected Tablets?
(It is a hypothetical question, because none of those things were created under market pressure.)