Anecdotal evidence: When I swim for distance underwater, and really push myself, I will often experience a strong compulsion to surface, even when I believe I can hold out for a few more feet and reach my goal. I am not even afraid of drowning, yet I consistently follow the compulsion to surface.
I can't think of a way to study this in an ethical controlled experiment, but data can be gathered from suicides and attempted suicides that would be relevant to the theory.
I have similar experiences when swimming underwater. I used to see if I could swim the length of the pool in one breath, and often would surface seemingly-prematurely out of a sudden strong desire to take a breath.
My old roommate reported having lots of trouble letting go of a handle when skydiving. He very much wanted to dive, and was not afraid of an unsafe landing, but instinct was very difficult to overcome.
Followup to: The Strangest Thing An AI Could Tell You
Brain damage patients with anosognosia are incapable of considering, noticing, admitting, or realizing even after being argued with, that their left arm, left leg, or left side of the body, is paralyzed. Again I'll quote Yvain's summary:
A brief search didn't turn up a base-rate frequency in the population for left-arm paralysis with anosognosia, but let's say the base rate is 1 in 10,000,000 individuals (so around 670 individuals worldwide).
Supposing this to be the prior, what is your estimated probability that your left arm is currently paralyzed?
Added: This interests me because it seems to be a special case of the same general issue discussed in The Modesty Argument and Robin's reply Sleepy Fools - when pathological minds roughly similar to yours update based on fabricated evidence to conclude they are not pathological, under what circumstances can you update on different-seeming evidence to conclude that you are not pathological?