Obstruction change of mind

[debeau]

Saw this recently at agame .
4 man team
PU watching runner going to first as runner comes into 3rd .
Runner goes past 3rd and gets tagged 1/2 down line to home and PU who has moved up that way to take the runner calls the out .
Meanwhile 3rd base umpire comes down the line yelling obst I had obst .
PU quickly kills the ball ( the BU didnt ) and talks with BU who states he had obs after rounding 3rd and runner should get home .
PU says hold on would the runner have made home if no obs .
Answer , no , ok we will have them safe on third .
PU walks away and base coach talks to BU and all of a sudden BU is telling PU , no I made a mistake OBS was before the base and the out should stand . Ok we will live with that but offensive coach is not happy .
How do you handle the situation and guess who gets the blame from a very partisan crowd .