15 to 20 years ago, I might have agreed with you, but I don't believe that our government will recognise any limit to their power any longer.
IMO, it is state law involved here, not federal. I guess there is no basis in law for the exemption in La which surprises me given its French based system.
Federally the specific issue is covered by law which would either have to be changed or overturned i.e. doctor patient, marrital, priest penitent and the like.