That point troubled me as well. I'm guessing that Michael, attempting to keep as much "official" distance from his New York underboss as possible, delegated routine contacts with the Police Department to Clemenza and Frankie (though I bet Michael still pulled strings personally with NY political pezzanovanti). When the cops found Frankie, as Tom said, he was "half dead, scared, talking out loud about how you betrayed him." Detectives might have concluded that, to induce Frankie to keep talking, it'd be prudent to hustle him away and keep his survival secret, lest Michael or someone else try to whack him.

As counsel to a Senate committee about to investigate organized crime, Questadt had high-level contacts in the NYC police who would have told him about Frankie. Questadt would have seen a huge opportunity for Roth, to whom he belonged. I'm guessing he convinced the committee chairman to use his clout to wheedle Frankie away from the NYC police and spring him on Michael in a guaranteed perjury trap.