I can think of a common situation where reaction time is the deciding factor in life or death:
A popular1v1 tactic is to run away while having an attack chambered, then suddenly spin around and release your attack at an enemy. If you want to actually catch the person, you can't run with a block chambered, you have to react with the block. This maneuver seems to execute in about 250ms. If your reaction time is sufficiently faster than this, you execute the block. Otherwise, you get hit.
I fail to execute the block in this situation at least 75% of the time, others never succumb to it. There is no other factor involved than pure reaction speed-no "battle awareness", "footwork", etc....just clicking in response to a visual stimulus.