This all seems very logical expect you're omiting one key thing: before strangling Pantangelli, the Rosato brother (played by Danny Aiello) tells him, "Michael Corrleone says hello."
If the Rosatos are acting on Roth's orders, why would they lie to Pantangelli about who ordered his killing? It makes no sense.
It was an ad-lib by Danny Aiello, and it made no sense, given that the Rosatos indended Frankie to be dead. So why did FFC leave it in? IMO, the line was not intended for Frankie, but for Richie, the bartender, whose ginmill was being used to set up Frankie:
It’s obvious that Richie is a “civilian,” not a Made Man, and he’s nervous as hell about his bar being used for a murder (“Carmine, NO, not HERE!” he screams at Tony’s brother (played by Carmine Caridi) after the cop enters and Carmine draws his gun). The Rosatos know that Richie might be squeezed by the cops investigating Frankie’s murder. Richie would be too fearful of the Rosatos to identify them as the killers. Still, as a civilian, Richie is not bound by the code of omerta. So they hand Richie something he can give the cops so that Richie can get off the hook: “The murderers said, ‘Michael Corleone says hello.’ ” That line would set the police after Michael, and would be picked up by the press-- another nail into the coffin of Michael Corleone’s “legitimacy.” Clever Roth!
