I think that when Sovereign Marouk watches the Enterprise going to warp from the window and says, "A fine ship, Commander!" that's pretty strong evidence that it's what really happens. :P
Except the only thing that really
happened was that some actors delivered scripted dialogue in front of a camera and some special-effects artists created some imagery. And sometimes that dialogue and imagery can't be taken too literally. Roddenberry himself was known to suggest that what we saw onscreen in TOS was not the literal truth of what "really" happened in the Trek universe, but merely an imperfect dramatization thereof. In his preface to the TMP novelization, he adopted the persona of a 23rd-century producer who'd dramatized the "real" experiences of Kirk and crew, and acknowledged that said dramatization had been "inaccurately 'larger than life.'" And when 1979 audiences asked why the Klingons suddenly looked different in TMP, he asked them to accept that the Klingons had "really" looked that way all along, but TOS hadn't had the budget and technology to portray them appropriately.
There are certainly many things that can be rationalized in-universe; I've built a lot of my career as a Trek novelist on doing just that. But there are some things that are better just chalked up to dramatic license or inaccuracies in the shows' interpretation of what, let's face it, is an unreal future that they're making up as they go.
Oh, you just love raining on my parade, doncha?
Anyway, if we're saying that things that didn't happen were portrayed as happening simply to make the episodes more dramatic, then I think the sudden danger of going to warp inside a solar system counts! *Grins*