I think there's a simpler explanation:
Frankie, just after his narrow escape from death, was "half-dead, scared, talking out loud [to the New York detectives] about how you [Michael] betrayed him." He agreed to sign affidavits for the Congressional committee about Michael's criminal activities. But he probably balked at the prospect of testifying against him in an open hearing, where he and his abandonment of omerta would be exposed to millions of his fellow Americans. So the FBI guys told him, "Don't worry, Frankie--ten to one he's gonna take the Fifth. That's tantamount to an admission of guilt. You won't have to testify." They may have meant it. More likely, they were in on the plot to trick Michael into perjuring himself by keeping Frankie's survival secret. Since Frankie was "on ice" at an Air Force base, there'd be no way he could know that his survival was being kept secret from Michael. There'd also be no way of him knowing about Cicci's testimony if they decided not to tell him.