Is it true that the winning team players are all team players?

That question was asked in the Dropping Knowledge Group at XING. My answer was that when I was tought to be a project manager, our supervisor built up certain scenarios ... we were all taken beside and we were each given a task to fulfill ... each of the participants was given a special duty on that "virtual project" and we were all confronted with each other ... no matter, the strongest had some kind of success ... but my feeling was that the team's final goal had not been served to at all ... ... looking at todays world and at certain markets I wonder if any issues can be resolved if all managers are tought to only look at their "sub" objective and not at the "global" goal ...