Correct.
The states have exclusive control, under the law, on who can access their election. AND, who won that election.
Congress has control over who is certified as the winner nationally.
After the federal election, the Electoral College and Congress become the only bodies that can judge eligibility and act on that judgment.
After the inauguration and the taking of the oath of office, only Congress can correct the problem via the impeachment process.
I wish John were still here. He brought a lot of insight into these issues.