I'll go by what Steve Belichick said about his son after SB 36.
I'll never forget the question and the response.
Reporter (I think it was Mike Lynch who asked it): "Did Bill convey any doubts or indecision to you about starting Tom Brady over Drew Bledsoe?"
Old Man Steve: (reacted as if he was insulted and about to hit Lynchie over the head with a hammer). "My son doesn't have an indecisive bone in his body.".
His decisions may be right or wrong but once Bill decides something, he goes with it.
There was no reversal of any punishment. If Josh was late the punishment was not a public thing (a fine, run up the hill 50 times, etc)
I firmly believe it was Bill planting fake news to rattle the media.