[officialtony]

This is an out at the very least. If I think she is signalling time due to injury, or if I think she got hurt on the play, we have Dead Ball and the runners advance no further. I'll take the heat for that call ( see related thread about coaches and injured players ). However, if it looked like nothing more than a train wreck and she was asking for time to stop advancing runners because she knew she couldn't get up in time to make a play, I am not granting time ( in your case, maybe that is what PU saw and thus, didn't want to grant time ).
Either way. in my opinion ( and remember, I wasn't there ), the out stands. The request for time was enough for me to see she had control.
Remember, I am not criticizing the judgment of your umpire. They were there and saw the play as it transpired and had the best view of what happened. They called it and that's the way it stood.

I am curious, what input, if any, did the BU have in this scenario?
Was there a discussion between BU and PU at all?
Sometimes that can help resolve a situation and save face at the same time - " BU had a better view of the ball and my call is the out stands. Catcher had control of the ball long enough. " Makes both umpires look efficient and willing to get the call right. Gotta sell it though!
Just my humble opinion.