Michael Corleone and Dr.:
Logic is on your side. My theory is far-fetched. But it's a fact that Geary was a member of the Senate committee, and must have known that they were holding Frankie in reserve to trap Michael. If he was in Michael's pocket, why didn't he warn Michael?
Logically, Geary should have realized that Michael was smart and would figure out his two-faced act and his knowledge of Frankie's survival. But when the blood's on the boil, logic flies out the window. Logically, Paulie should never have concluded that he could betray Vito and get away with it, but greed overcame logic. Carlo was crazy to think he could pull that beating-Connie routine twice and not get blamed for Sonny's assassination--but lust for revenge made him crazy. Geary, as a US Senator, thought he was invincible. Probably he thought he could fool Michael. And if Michael were convicted of perjury, than the credibility of anything Michael said against Geary (as in the brothel murder) would be compromised.
SB: Prostitution has never been illegal on a statewide basis in Nevada. Today, licensed brothels exist in 10 of Nevada's 13 counties. In the late '40's, the gangsters who were building Vegas lobbied the state legislature to outlaw prostitution altogether. They piously declaimed that prostitution was sullying the state's "respectable" reputatation. Of course, they were just trying to prevent anyone else from getting between them and the suckers' money. The legislature responded by outlawing prostitution in counties with populations greater than 500,000, which at the time only applied to Clark County (where Vegas is located).