I didn't read it exactly that way but perhaps I misread. Perhaps I was simply trying to generalize his principle.
If you want a Story Now game as your top priority then sticking with D&D would not be a good plan in my opinion. That does not though mean you couldn't add in elements of Story Now in places. I think system does matter as someone mentioned above.
What perhaps I missed is the posters desire to stick with D&D. I assumed that was because he primarily wanted to do D&D things and of course he is familiar with the system. He just wanted to add some elements from other games. That is great and with that goal in mind I think it can be done. If he was wanting to just do a Story Now game though I believe he'd be better off playing a different game.
There seemed to be an implication that D&D was just really super flexible and so there was no strong reason to use another system, at least if you were doing "D&D stuff, including some things that other games might focus on." Obviously if you want to do one single mystery story and the rest of the game is classic D&D, even at the planning level you'd probably not want to choose to use Gumshoe for the campaign. I think that's obvious. It seemed like the OP developed this more to "since some people have managed to do pretty much everything we can name in some D&D game successfully, D&D is fully capable of all these things." which I think was less justifiable.
It was pointed out that having no support for something, beyond maybe there's a skill check mechanism that could theoretically be deployed in any situation, doesn't equate with support. Again, "someone did it" was then said to be incontrovertible evidence that said thing "is supported." We all obviously mean very different things by that word, 'supported'.
I mean, by this definition Traveler supports Vancian Spell Casting. It certainly doesn't PREVENT it, you could make up some houserules to do it! I think that tied into the side discussion that
@loverdrive started about the way even the most thoroughly hacked D&D is still called 'D&D' and this makes it pretty hard to say what D&D does and does not support.
My own line of argument has been that if you want to have support mean something, then you need to have actual process and agenda/principles which support it, because a disconnected mechanic like 5e's skill system has no traction, it doesn't decide anything. Meanwhile general resolution systems that DO have said process DO have traction (or as
@pemerton puts it 'teeth'). So it is hard to say that an RPG with such a system doesn't support a LOT of things, though specific games may be pretty narrow based on the actual details of implementation. Still, a game like 4e seems to at least provide a ready-made structure to handle most anything, so how is it not 'better support' than just 'maybe you can make a skill check for that'?