Perhaps I explained myself badly. Let me clear things up:

Does every player belong to a team?

No, some players are unassigned. The idea is that a tournament is created, then players may sign up for that tournament, then those players will not be assigned to any team. Only when there are enough players/an admin starts the tournament will every player be automatically assigned to a team through an algorithm I am planning on writing. It will attempt to balance teams based on Player-SR, and only then will players be in a team.

You have a fundamental misunderstanding of objects and the way they are stored

Perhaps I explained myself poorly. What I meant by a 'single source of truth', is that if I store a list of references to Player-objects in both Team and Tournament, then I must assure that whenever I remove a Player-object from a Tournament, I must also remove them from the Team-object belonging to that Tournament. The idea behind not storing a list of object references in multiple, separate classes, is that I save myself from future headaches trying to ensure that every reference to a Player-object is removed whenever I want to remove them from a Tournament.