Not even close: Not only is that story false, it completely erases how a) this was a well thought out stunt put together by an experienced stunt team and b) the stunt woman in the scene designed the stunt expressly to keep her from drowning at the hands of confused crew people. But don't take my word for it, start watching the behind the scenes video below at the 20 min mark and hear it from the woman herself:
Why is that a problem?: Stories like these remove agency from the actors on screen. If we write these performances off as reactions rather than honed skill, we're implying that those people aren't capable of being skilled in these areas. That's pretty messed up.
Not the only example of this kind of thing: The instance that got me thinking about the possible false narrative of that Jaws scene was the story of Will Smith on an infamous episode of the Fresh Prince of Bel-Air. Many times I'd seen that this was just an accidental breakdown on Smith's part while recalling his own father leaving him when he was a kid. But that's not true either. According to a well sourced and epic take down of that lie by a tumblr user (that I cannot find now of course) that features this Uproxx article, Smith's father was nothing like his character's father. Smith was actually using unrelated personal experiences to inform his character's emotional response in that scene, just like every other actor on the planet does.
Question everything: The next time you hear a behind-the-scenes story about a particularly real scene in a movie, tv show, or the like that credits the realness/rawness to something other than talent, dig a bit and see what you come up with. And shut those lies down if you turn up that it's false!