I can't help but wonder if these experiences are a natural defense mechanism. When confronted with a sudden danger, our brain fires up to maximum capacity, quickly searching all of our memories for a way out of the problem (making our lives flash before our eyes) while simultaneously thinking so fast that time seems to stretch out in comparison.
We only seem to be able to access these abilities in times of great stress. Still, it's interesting to think about what our minds are capable of doing. What if we could access our brains this way at will?
I think that this could make for a decent story idea. I know that movies have at least represented the idea of time slowing down or standing still, but this more realistic type of superhero story might be an interesting take on the genre.