First I agree with your above statement, tact is required. I would fully support a players right to say "I don't agree with my owners stance on …….." And if the owner and player sat down and agreed that they move on, that's fine too. But I disagree they are on equal terms. One is the employee, one is the employer. Unless the employer is mistreating, is abusive, creating an unhealthy work environment, etc... then I don't see ground where the employee can dictate his contract is no longer valid.
And yes its a contract, not indentured service as you said. But that contract says, I will play NBA basketball for Team A for the next X number of years. He can opt not top play, but then not get paid. JMO, but I believe the NBA has give too much power to players. They on a whim can completely dictate what a coach/GM/owner will do because they have the leverage. And this is now (sounding like but not confirmed) including "because he voted how I don't like." And this goes both ways, what if an owner said he wasn't going to honor a contract because a player voted how he didn't like? People would be up in arms. People just need to man up and start solving differences like adults.