The problem is that there’s such a belief that the rabbanim are ALWAYS right that it’s pretty much impossible for one to admit to being wrong- and not just from his perspective. I can completely understand if a rav was against this family due to misinformation (dlkz) and now, he suddenly realizes that he was wrong and is probably miserable right now. I know I would be, personally. But honestly, to those people who surround them, the admission that their leader is wrong would come out as a betrayal, as many above have mentioned.
An apology would bring back one amah the people who had already stepped back two amos, and it would push the others back two amos. As far as PR is concerned, there’s really no way to come out of this unscathed, but chances are, it would be WORSE for their image to apologize, sad as it may be.