When you're about to hit something, "jam down hard on the brakes" is about as close to "instinctive" as anything can be in a learned activity like driving. That's why they spent all those years teaching "pump the brakes on ice". (Now of course wrong when it comes to anti-lock.)
If I hit the brakes and it didn't slow down, I'd press harder until either the pedal or my seat-back broke loose. (I bent a seat that way once.) I really didn't think I was that much in the minority, but all these people talking about their UA experiences, I don't hear them saying, "I stood on the brakes as hard as I could." I hear, "I tried shutting it off, I tried downshifting, everything I could think of." Which seems not to include using the damn brakes.
Okay, one did say she engaged the emergency brake. Do they still call it that? It's been the "parking brake" on every car I can remember.