The 10th amendment doesn’t change the supremacy clause. It simply makes explicit what’s implicit in the supremacy clause: federal law takes precedence over any and all state laws and constitutions when they are made in pursuance of the US Constitution, so the 10th amendment clarifies that if it’s not a power granted to the federal government by the US Constitution, then it’s reserved for the states. To invoke the 10th amendment in this case you would have to prove the federal government is acting beyond its constitutional scope, which would require either proving it’s going beyond EMTALA or that EMTALA itself is unconstitutional. They are not making either claim in this case.
The 10th amendment doesn’t change the supremacy clause. It simply makes explicit what’s implicit in the supremacy clause: federal law takes precedence over any and all state laws and constitutions when they are made in pursuance of the US Constitution, so the 10th amendment clarifies that if it’s not a power granted to the federal government by the US Constitution, then it’s reserved for the states. To invoke the 10th amendment in this case you would have to prove the federal government is acting beyond its constitutional scope, which would require either proving it’s going beyond EMTALA or that EMTALA itself is unconstitutional. They are not making either claim in this case.