If Frank is around Tristan, he's going to know he's not really what he claims to be, and probably approach someone such as L or Will to see if they agree. But I agreed with Jazz I could keep him away from Tristan if need be. Or he could approach L in particular and L could say Frank is wrong (because of blackmail or any other reason), in which case he would drop it for a while at least... because I obviously don't want the plot ratted out from the beginning either.
Frank actually likes Jazz and feels he owes him, but I don't think that helps here as he doesn't like him quite enough to do something he'd see as betraying Asgard. (It's more like if anyone threatened Jazz's life Frank would probably defend him.)