It's not as if Picard was buying into anything these folks were telling him. The HQ was Picard's established enemy from the moment he chose to believe Keel and sail to Earth, and he went there to confront that enemy. At most, he suspected Quinn might still be an ally - but since Quinn was apparently keeping secrets from the other two Admirals, it was pretty much certain that the two were hostile and, since they were pretending not to be hostile, deceitful to boot. "The place is a bit quiet because it's Hide In Your Room Night" is something Picard would merely nod and smile at, because he'd recognize a lie from the fact that Aaron's or Savar's lips were moving.
Remarkably, Savar feels the need to introduce himself and Aaron to Picard, suggesting these folks are relatively low-ranking nobodies rather than Picard's well-known top bosses. Which works well enough if we assume the pipless flag rank is the lowest (either Rear Admiral or, if we assume future Starfleet customs call for addressing a Commodore as Admiral, then that rank), making Savar a Vice Admiral and Aaron an Admiral at most, but allowing them to be Rear Admiral and Vice Admiral, too.
That Savar speaks for the trio both in the viewscreen introduction and during the dinner does suggest the bug within was the boss. Might have been Savar was possessed by a Bug Grand Admiral. Might be Savar was a Bug Corporal, and the bugs placed relatively little emphasis on the occupation of SF HQ and the capturing and interrogation/coopting/elimination of busybodies like Picard - the real action might have been elsewhere at the time. After all, if SF HQ was being kept empty, it couldn't have much role in misleading Starfleet, either - it would need to be busy to accomplish that!
Timo Saloniemi