I buy TB's minority view on Geary. Consider:

1. Willie Cicci openly admitted to Questadt that he was a "button" i.e. that he killed people when he was ordered to do so.

2. He then told Questadt that he never got an order from Michael, but he confirmed that Michael was the head of the family.

3. At that point Geary interrupts Questadt and asks Cicci to "amplify" his answer and the back and forth about "buffas" ensues.

What is going on here is a tag team approach by Geary and Questadt. If Geary wanted to stay under Michael's thumb he would have excused himself for his other committee meeting, and made his speech about how we should not judge all Italians by "a few rotten apples" without getting Cicci to admit there were beffers between him and Michael. The buffer of course was Pentangeli, and Geary had to know that Pentangeli was alive and ready to testify.

Being savvy, however, once Geary did this bit of dirty work, he leaves the scene to give himself some cover in case things with Michael do not go as planned. On theother hand, if they do, and Michael is fighting perjury counts, the blackmail against Geary is worthless. Some allegation about a past incident with a hooker -- that had been covered up --
would not fly if it came from the camp of a perjurer. It would look desperate, and Geary would be useless to Michael.

It may well be that all Michael ever wanted from Geary was to move Klingman out and cut Geary out of the profits, which he'd already accomplished. Still Geary damaged Michael in that hearing but gave himself enough cover by leaving the proceedings to defend himself should things come to that. N.B. Michael did not include Geary in his plan to wipe out all his enemies.