Anne I don't know whether the judges have fallen out with their bosses, but it seems that way. They probably don't like to be gagged to have favouritism but put up with it for the money.
There might have been some attempted manipulation of the judges by the producers. Who knows? But whether there was or not I doubt if they were told to remain seated after the result was announced and I'd be very surprised to learn that Robin was instructed to post an opinion on twitter that questioned Beth's right to her success.