I agree that FBI records are spotty at best, filled with hearsay and uncorroborated information. And, yes, their knowledge of the Mob was sketchy through the early Sixties. But, it's been pretty well established that Liston hooked up with the St. Louis Mafia early on, and that his contract was bought out by Frankie Carbo. So, it's not unlikely that he threw the second Ali fight on Mob orders.