Ovinomancer
No flips for you!
If you're talking about moments of play that fit the Story Now agenda, they have to happen either by complete accident -- in which case they are passing -- or bloody-minded intent on the part of the GM. And I mean bloody-minded. This is because the structure of play in 5e will not cause these moments to occur just through following how the game tells you to play and provides means for you to play. The core loop structure of 5e -- mentioned on page 4 of the PHB and reinforced elsewhere -- cuts hard against Story Now play emerging. The mechanics of the game mostly point to simulationist resolution because they resolve at the task level and tell you if you succeed or fail at the task only. Inputs are only those that relate to the task, and outcomes are only about the task. Take climbing a wall, for example -- the only inputs here are the GM's assessment of the challenge of actually climbing the wall and whatever things the player can bring to bear (like climbing gear deployed or assistance from a fellow). The result of this check just tells you if the climbing task is successful. Anything downstream of this -- like say if you're climbing to get to the top of a cliff to stop a terrible ritual -- is not going to have anything resolve here (and shouldn't, given the inputs), but failing may invoke some other timekeeping loop that may result in an eventual failure to stop the ritual in time.I am not quite sure all have acknowledged that, but sure, I agree with you that this is the distinction. This is a thing that can happen in 5e, but the game is not designed to make sure it will. This is absolutely fair.
But I'd argue that it commonly happens, albeit obviously not to the frequency and degree people who prefer Story Now games would like. But in practice players tend to have great freedom in defining their characters, including their backgrounds, hopes, dreams, convictions and fears. And usually at some point some of these will be challenged in the play, either due the GM paying attention to these sort of things and making it happen, or the situation just emerging randomly.
And I do not at all argue that this makes 5e and Story Now games similar as overall experience, but that these specific moments still share a clear similarity.
So what does all that mean? 5e's mechanics cut against Story Now play at worst, and at best have nothing to provide that aids Story Now play. To get to a consistent experience of Story Now play, you pretty much have to heavily houserule. You could have momentary Story Now play, if the GM is super duper keen and brings everything with that and the players pick up (or it's clearly communicated) so they can hold up their end, but this is a huge overhead on the GM with no support at all from the system, only hinderance. You might do it, but it will be inconsistent, will be constantly fighting with the system (and throwing incoherencies all over the place), and it's mostly not worth it when you could get a game that does this kind of play sooo much better. You might accidentally stumble into a few moments, but that's unlikely given how much the system pushes against Story Now.
And the reason I say it pushes against Story Now is that the system tells you that the GM Says. And the GM Says with very few restrictions. And, as I noted above, the mechanical resolution actually often relies on the GM's say to operate (picking a DC is entirely up to the GM, which puts pressure on the pass/fail envelope). And, probably most notably, the GM is not constrained much by the outcome of checks by the rules (individual GMs can do as they please -- I do, and always honor the result of checks). They can see a success but narrate an outcome that might hit success by the letter but certainly not the spirit and they would not be playing one whit incorrectly (there are a few instances in published APs I could point out where this happens and isn't being malicious).
So, yes, is it possible that 5e has Story Now moments? Sure. Is it likely? No, not without serious intent and effort, and then irregularly.