Based on what we know from other episodes, I speculate that the "The Ultimate Computer" writing and/or production team consciously decided Wesley really worked for Starfleet Command and was given temporary command of the Lexington just for this special mission (I say special because nearly half of the starships in the fleet were involved!) and conveyed that to Theiss.
More likely someone in the wardrobe dept. remembered that previous commodores (or four out of five, anyway) wore the Starbase/Starfleet Command badge so they went with that and gave it no more thought.
I still think the simplest explanation in-universe is that Wesley was CO of Lexington
, like Decker and Constellation
, but as he was acting in a higher capacity as task force commander he wore the badge associated with higher command.