I did consider that, but if Starfleet truly didn't want an android to have any kind of authority, they never would have allowed him to become a lieutenant commander. He stayed forever an ensign like a certain someone...
Honestly, Picard loves a hard luck case, other notables including Worf, Sito Jaxa, & Ro Laren, etc... people who might not otherwise get a fair shake elsewhere in the fleet, because of who or what they are.
I have no issue figuring Data was also one of those situations, where Picard took him, specifically to give him a shot he was never otherwise going to get. Data spent 12 years at Lt. & 4 at Lt. Cmdr, before the Enterprise, a total 19 years active duty, to Riker's 7 years to getting offered his own ship,
Data was languishing, & I'd hazard a guess he only got that rank bump because someone wanted to put him to greater use, for his vast computational capabilities. He was likely going to be relegated to being a huge computer or tech resource for Starfleet, but that move maybe brought with it a major responsibility that warranted a rank increase, which he maybe petitioned for himself.
So they gave it to him, to appease him, never suspecting anyone would be crazy enough offer him a post somewhere that leadership was possible... Until Picard. Even Troi was a Lt. Cmdr, & is never seen in a command role but for one unusual crisis. Sometimes the rank is somewhat honorary,
Data is much more special to Starfleet interests than Harry Kim, & that might likely have gotten him a bump or 2 for utility reasons. However, Picard is a champion for lost causes, & looked on a near 20 year veteran, deciding that this guy deserves at least a chance at commanding, if he's interested in it, & everybody probably thought he was nuts for doing it.