I think this has been addressed before in this thread, but I cannot find exactly where. Also it never hurts to have a refresher:
P punts the ball at R's 35 yd. line.
P1 pops up the punt, and it hits the ground at R's 34 yd. line.
Ball bounces backward where P1 catches it at R's 37 yd. line.
Officials blow the play dead as soon as P1 caught it.
Correct call, or would P1 have had the opportunity to advance the kick since he recovered behind the neutral zone? Incidentally, I did not see anyone on the sideline yelling at P1 to run with the ball after he caught it. It looked like P1 had a clear path down the middle of the field to at least get the 1st down.