If the nails were in a tree, it was by accident. An emotionally disturbed white suicide who only wanted to kill himself in an oddly public way would not have needed shrapnel, as the explosive on his person would have killed him instantly. Since this was Just a Suicide, there couldn't have been nails. So, probably there just happened to be nails near his bench, that just got caught up in the explosion, and thats how they got in the tree.
Got it?
Maybe a strong minature tornado hit an Ace Hardware store close to the suicide site.
When the bomb went off the 16 penney nails were circuling the poor student and that caused them to penetrate the tree.
Regardless as you noted, it was just an accident or it didn't happen.