Ultimately yes, he is the boss, and as there is no rule that says the doctor can order the player off if he passes these quite frankly bizarre tests that exist in the bubble that is professional football. Even the PFA are calling for laws that mean automatic substitution if knocked unconscious.
If someone in the office fell over and was knocked unconscious would you as their manager dust them off, ask them if they are ok and sit them back down to work or would you send them home via the doctors?