1) I like umpires that make sure that the proper call is made, regardless of who's supposed to own the call. In that specific situation, I would have preferred the FU to make a call one way or the other -- even if he had to guess. Then, after calling time, run down to the PU to seek his input. Then, make a decision to keep or overturn the original call. I have no idea if what I described is proper mechanics or not. But, I think it's maybe not a great thing to immediately put the PU on the spot for a play he may not have thought was his to govern (and, therefore, may have not watched it closely enough).
2) There's another thread here that goes into great detail about when an out is recorded officially, in terms of baseball control and release. You didn't specify what rules governed this game and this could be important, as there were some differences between the various rule books. I'd recommend to always state explicitly the governing rules when asking for rules interpretations.
The umpire appeared to see the following:
- Catch
- Tag
- F5 reaches into his glove to remove and throw the ball
- F5 drops the ball attempting to throw to F1
You state: " I thought that exchange rule was if an infielder was attempting a throw to another base, [... and] drops the ball while attempting to throw [...]" I'd replace "base" with "fielder," as players never throw the baseball to a base or any other inanimate object (not on purpose, anyway) -- they may use bases and other objects as aim points, but the expectation is that they're throwing so that another fielder will catch the ball ... players throw to other players. Anyway, I agree and so would the umpire, it seems. And, in the umpire's opinion, that's exactly what happened. The umpire ruled that *after* the controlled tag, the F5 was attempting a throw to another player and dropped the ball while attempting to throw.
This seems less of a rules interpretation and more of a judgment call. May have been a bad call, but the application of the rules seems correct.
I've seen what you describe and I've seen the opposite: 4-6 force at 2B, FU calls out, F6 slides off bag, retrieves ball, attempts throw to F3, ball flutters up and falls down at F6's feet. F6 bobbled the transfer attempting the throw to F3. Umpire rules he dropped the ball, overturns his call at 2B, all runners safe. Was it a terrible judgment call? Yes. Was it a rules interpretation issue? No. He correctly applied the rules to the situation as he saw it unfold. He just happened to see the play differently from literally everyone else at the field. :-) I would guess this is the same as your call at 3B.