I think the definitive factor is temporal. Collectivism is working for a more distant future usefulness to place (and people attached to a place). Teamwork is competitive in here and now selfishness.

The sports mantra goes, "There is no 'I' in 'TEAM'!".

Mine goes, "Without 'ME', there's no 'MEAT' in it."

"How can we help you get your part of this project done sooner?"

"You can't. You have nobody with my specific set of combined skills that can do what my part is."

"You just aren't a team player."

"Agreed. I'm a serious team."

-Actual conversation: but I left out the profanity. ;)