I don't think players should be have the right to shut themselves down. Not unless I can shut myself down from work for a few months because I'm uncomfortable.
If a player feels he is physically unable to perform even if the team's medical and training staff clears them, I think its their absolute right to shut themselves down and not play. The doctors and trainers
1. Don't always prioritize what is best for you but what is best for their employers
2. Don't always have the correct diagnosis down.
Players know their bodies. They know when things aren't right even when the doctors say everything is okay to go. The players should never feel they absolutely have to play if they feel they aren't physically able to go
But when players can decide the conditions under which they'll play, that creates a slippery slope. There's a lot of room for the athlete to take advantage of that.
Is it status-specific? Can an all-star choose to sit if he/she doesn't feel 100%, but a role-player is expected to suit up until the wheels fall off? The NBA, in particular, is truly a league run by the highest profile players. I think they'd succeed in a mutiny.
Or profession-specific? If I stated a need for a work hiatus: 1. It'd require a strong rationale with supporting documentation, 2. If honored, it'd prob hurt me long-term. Even in a more minor situation... If you were my boss, and said "tar, we need a report within 6 hours," I'd say "I'll get on it, nick." You'd reply in typical nick fashion, "You better, idiot!"
Injury severity-specific? I'd support a player shutting himself down to avoid a serious long-term injury. For example, a player that doesn't feel ready to return from a concussion (I think we actually talked about that once). Athletes are paid (very well) for a service with certain expectations. While I don't advocate for long-term risk, they chose the profession.
I think there's merit to it under certain circumstances. But there's a lot of gray area and it's ultimately an ethical issue. I always worry that when a lot of money is involved in any decision-making process, there's an increased likelihood of foul play, too. Sometimes these reports don't add up, and other times, the player just blatantly neglects his duty.