I would agree with you on the team listing. The way I read the rules, it should be the NBA team, not the college team since the college team is not actually listed on the card--the player is simply shown in his college uniform. According to the FAQ:
"If the player is pictured in their college or minor league uniform, but the team listed on the card is their professional team, the team that gets put into the database is the team listed on the card."
Since the handful of cards I looked at list ONLY their NBA team, that is what should be in the checklist (I assume the others are the same).