It's a NATO task force, and it has a rotating command. Like all military task forces, our commanders have the treaty-bound right to refuse participation in any order or exercise that contravenes the will or laws of the United States. It's really not a big deal.
If it's not a big deal, why have people complained about US ground troops being assigned to a UN contingent in Europe during Clinton's term?
I just happen to think our Constitution states that our troops, ground, air or naval, should answer to our President and only our President, not some officer or leader of another country.