To compromise Geary it would seem all they needed to do was to get com photographs of him with the hooker, and some statements that he was a regular there, and into really kinky game playing, and they would have him by the short hairs (especially with the Corleone's people in the press). So why did they have to kill an innocent person to further this agenda? IS this supposed to show how much more brutal Michael was than Vito? After al look at the trouble Clemenza went to just to make sure "pain in the ass innocent bystanders" didn't get hurt.
A scenario had to be created where Geary would be absolutely OWNED by the Corleone Family. Legal or not, the prostitution itself would've been pretty bad for a U.S. Senator, but not quite enough to have him by the balls like they did. Anything other than cold blooded murder he might've still found a way to be resistant. They needed him in office and in their pocket.
And yes, Geary knew he didn't do it and eventually did realize he had been slipped a mickey & set up BIG TIME by Michael Corleone. It's written all over his face after Cicci jokes about that 'buffer' question.
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