Honesty is the best policy?

[fguyton]

In the last two weeks we've had two games with similar situations that I'd like to hear some opinions on.

1) R1 coming home, there is a throw to the plate. F2 receives the ball and makes the tag but drops the ball as the tag is being applied... but picks it up quickly. PU is shielded from the drop and rings up R1. F2 (much to dismay of Coach and parents) tells PU "He's safe, I dropped the ball." PU asks him to repeat it, which he does, and PU changes call to safe.

2) BR moving to get away from high inside pitch. Ball nips the bat but hard to tell if it was bat or helmut. PU calls HBP tells BR to take his base. BR tells PU it hit the bat not him. PU changes call to foul tip.

At first I thought these were the best ways to handle the situation, but the more I considered it I became less sure. What if if were the other way around, i.e., 1) F2 says "I didn't drop the ball" when PU thinks he did, and 2) BR says "it hit me not the bat". Would the PU change the calls then?

How should you handle something like this?