I think what people are getting at when they say that "indie" games are more focused is more that the mechanics are weighted to produce a certain nebulous feel, whereas other games tend to work in broader narrative contexts.OK, so just to clarify what you're saying -- you're finding that people are claiming Edge of the Empire is flexible, and Apocalypse World is not? I mean, we both know the opposite is true, but you're experiencing a more than expected number of people claiming otherwise?
For example, look at Fate. Fate is strongly based around the use of Aspects, both having them compelled in order to get fate points and activating them yourself to get bonuses. So in a typical Fate game, you will get into a lot of trouble just because of who you are (gain fate points) but in the end you'll come back and eke out victory by calling on your reserves (spending fate points). This can apply to lots of different environments: urban fantasy, pulp science-fiction, martial arts competitions, time-traveling cosmic horror, and so on, but they'll all follow a similar beat.
In a way, you could say that playing a system like Fate is like watching an episode of Blackadder (at least season 2-4). You know that when you're watching an episode of Blackadder, you're going to see a lot of snappy dialog, Edmund Blackadder being amazingly snarky but in a situation where he is somehow dependent on the favor of some superior (Queenie, Prince George, General Melchett) and Baldrick being an idiot that occasionally comes up with plans and is continually abused by Blackadder. There will be some characters that show up in some seasons but not in others, but each episode has a similar structure even if the details differ.
By contrast, a game of Age of Rebellion has a lot of variety in structure and plot, even if the starting setting is the same. You could be infiltrating and assaulting an imperial spy base. You could be negotiating deals with locals for support. You could be going on a hunt in order to impress some other locals. You could be doing a heist on an imperial supply depot in order to get supplies for your base. You could be rescuing a rebel code-breaker from imperial custody so you can make sense of the intel you're getting from your base. You could be trying to stop the Empire from learning what's going on with the base. You could be defending the base from an attempt to reclaim it. That's a lot of narrative variety, even if they are all based around "You are a team of Rebel operatives."
Of course, I wouldn't use D&D as an example of a "flexible" game. D&D has a lot of assumptions hard-coded into the game, notably the whole Zero-to-hero progression, and a lot of world-building being assumed by the rules such as gods granting their followers magical abilities.