In sports, being a team player would mean something like you don't play football as if its all a one man show.
But at work isn't this kind of independence a desirable thing? Like salespeople who have to carry their own weight at all times?
At this point, looking at all these job ads is giving me the impression that what it really means is "submissive and obedient".
Pretty much. Similarly, "passion" can be translated to "willing to work unpaid hours and/or low wages". As if the main reason I work isn't for the paycheque.