How does being trapped beneath the tree help Gradwitz and Znaeym arrive at a reconciliation?

It does seem odd that the men reconcile only after being pinned down underneath a tree.  I think there are two reasons why this happened. 

First, the men are badly hurt.  Ulrich probably has broken legs.  The text states that his feet would have been broken were it not for his heavy boots.  Georg is also hurt.  In fact, he is bleeding from his head.  The blood is over his eyes to the point of impairing his vision. So, they are probably thinking of their own mortality.  When a person contemplates death, things are put into perspective.  In the face of death petty things are really seen as petty.  So, their quarrel is minimized. 

Second, the men are forced to stay together for a prolonged period of time.  This enables each man to see the humanity in the other.  When this happens, you cannot demonize the other person.  In other words, when you see another person as a fellow human, you are more apt to show compassion and befriend them.