Whatever it is they have on Roberts, its knowable. If the black hats have it, the white hats should be able to determine what it is and either free him up from blackmail, or simply present it to him directly and force him to resign.
In any case, he needs to go. He is subject to improper influence and that means he has to go... but he will only go if he is more afraid of the white hats than he is of the black hats.
If it got out that he was being sandbagged for cause, wouldn't that make all the cases he has ruled on invalid? What a mess.