Actually, he might be right. I thought i vaguelly recall an episode (in season one perhaps?) where it was stated that Troi was just a civilian. But who knows, its clearly obvious later that she is indeed a Starfleet Officer. hell, by the end of TNG, she is a full Commander! In my opinion, I would have to imagine her as a Starfleet Officer becasue she technically has Medical skills much like the Cheif Medical officer. I find it highly doubtful Starfleet would not want even its councelers to be Starfleet personel. In an emergency, Troi might know basic medical skills in her Academy (or whatever Starfleet Training) she may have gotten. And this brings up another point, do all Starfleet personel HAVE to go through academy training? We see in many episodes (even Cheif O'brein) that you don't need to go to Starfleet Academy to get into Starfleet. Perhaps Troi went though an "ROCT" school or something like that that was in conjuction to her schooling in Medicine/Psycology. She might not be the best trained officer in Starfleet, but enough to be considered certified. Heck, right now I'm working on a Federation Police Cutter Model (from SFB) where the design is based off of a concept I have always thought the Federation would have. Why not a type of "Guard" branch that works similar to the Coast Gaurd we have today? If you had a branch like this, you might need a lot more personel to fill in roles of the Federation that Academies couldn't provide (ie. Enlisted men, Non-commisioned officers, "ROTC" type of Starfleet Officers, possible Civilian experts, etc.).
man, I'm getting off subject here. As for Troi's use on the Enterprise, during peace time, I could easily see her role as being useful, but during times of War, probably not, unless she has enough other skills to be useful in a war effort.