You’re saying ad hominem isn’t valid as a counterargument, which means you think there’s an argument in the first place. But it’s not a counterargument at all, because the LLM’s claim is not an argument.
ETA: And it wouldn’t be ad hominem anyways, since the claim about the reliability of the entity making an argument isn’t unrelated to what’s being discussed. Ad hominem only applies when the insult isn’t valid and related to the argument.