Maybe Picard is recognizable, because of the Locutus thing, but do you really think the rest of the crew would be? I mean, I know that the Enterprise has gone on some "notable" missions, but the Federation is pretty big. Does the average Federation citizen pay attention to the "military" a.k.a. Starfleet? I don't think that the average American would have any clue who serves on American aircraft carriers or any other Naval vessel...
Don't forget Admiral Prescott (I think) pointed out Riker's good work against the Borg
. I think that was general knowledge and not something he read before arriving.
Regardless of whether the Admiral read a missions briefing or not, I am sure that it was more common knowledge amongst Starfleet Admirals who led the mission rescuing Picard / stopping Locutus / saving Earth. Sure others might have known that as well, but would have been more surprising if Starfleet brass did not know
who led the mission saving the day!
BTW, this thread is making me want to watch Best of Both Worlds Part I & II!!