Yep and they just handwaive it. They assert the other sections are held against the states so this must be too. They also assert that only Congress has enforcement power for it despite nothing in the amendment saying so. It says “Congress shall have power…”, not sole power, not the power. There is no exclusionary language to preclude a state’s normal constitutional right to run it’s elections. Instead this adds Congress to the list of bodies that can enforce this.
The remedy for a state running an improper election is also not the supreme court. It is Congress, as laid out in the Constitution they supposedly are experts at enforcing. And yet they keep giving themselves major powers not in Constitution.