

This is partially true. State Parties do own party affiliation on a ballot. Many states have codified party affiliations so you can only run as Hitler (D) if you have won the State Democratic Party Primary. But if you don’t win the Primary, you can still appear on the Ballot, you just have to run as your own party, or (I) or whatever. You can certainly still call yourself a Democrat, or a Republican, or whatever, but how you will appear on the ballot won’t be under the democrat ticket.

For the primary the Party can choose to disqualify a candidate from being able to run in the primary, but obviously that has to be done before the primary, once that happens it’s too late and there is no mechanism to remove a candidate once the general ballot has been certified.