I can relate to this from rock climbing. Typically one climber at a time leads while the other belays (manages the rope). The leader is the one at physical risk but the most scared I've felt has been belaying.

Being the belayer means you don't have much control and are mostly just watching closely and hoping your buddy doesn't get hurt. Being in a scary lead situation forces you to concentrate which pushes a lot of the fear emotions aside. Worry and fear take a lot of energy, energy which often can't be spared in an emergency where you have some control over the situation.