No, it’s not.

There’s a reason they’re called sports franchises. When you join a company, the company has a right to move you another franchise within the company. You still get paid by the company, and you still work for the company. Just a different franchise.

Players play for a franchise (team) within a company (the NFL). The franchise can choose to take the player off their team and move them to another team, just as any Subway franchise can move their employees to another franchise in exchange for another employee who would fit better. You can refuse, but you’d likely have to quit the company itself (retire/buyout), unless it’s in your contract ( no trade clause).