On the bubble

[Wahoo]

Live $55+5 tournament. Down to five players. Four places pay. BB has more chips than the rest of the table combined and is playing loose and poorly. Blinds of T300 and T600. Chip counts approximate. (Neither player in action below is me -- I am SB and finished second in tournament.)

UTG (about T5000) folds.
MP about T5500) goes all in.
Button (T3000) folds.
SB (T6500) folds.
BB (T30000) calls.

MP has KK. BB has Ad 5d. BB catches an A on river and wins. MP was 2-1 favorite and could have been a much higher favorite given the range of hands BB was calling with. Does anyone not like this play? I think I probably would have done it the same way (or certainly, I would have been all in after the flop). How should being on the bubble affect decisions here?

Note: Two diamonds came up on the flop, so in retrospect BB would have called an all-in even after the flop and still won on the river.

Thanks for your thoughts,
Wahoo