Originally posted by Turnbull:
...as we saw so many times in the film, people bent on revenge (like Carlo and Fredo) don't think logically--and Geary had every reason to want to avenge himself on Michael.
After being caught in that brothel with a murdered prostitute with whom he had '...done it before...', and subsequently saved by Tom Hagen himself...I don't think Geary was in any position nor would he have a desire to 'avenge himself' on Michael.
Even if he later realized it was a setup (which he probably did)...they had too much on him and even a Michael Corleone in prison could pull strings to disgrace Geary and end his career in politics.
Apple