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Yes, they can. All your doctor can do is give recommendations to military commanders. Doctors are not commanders and have no legal power to bind a commander in any way.
I know this is no consolation to you, but if you are re injured based on your command's decision to require the move, that would be a decision that would be heavily scrutinized and that commander would likely see his future career harmed by that decision.
Unfortunately, that is the law works with command discretion. It can't be questioned up front on issues like this, only after the fact.