I must say I am a bit mystified by a person's willingness to destroy his credibility with the inability to admit error in things that should, actually, be of no importance at all.
I am, for example, a great admirer of Mr. Rogers. There is an urban legend that he was a Navy Seal, which he was not. It's a lie. If I had once held that view, it would be a stupid thing to hold on to it, after seeing considerable evidence that it was untrue. It would also, I believe, be stupid to believe that letting go of that lie would invalidate my admiration for Mr. Rogers. If I were engaged in a debate about Mr. Rogers' influence on children, throwing in a gratuitous lie would do me no favor.
What such obstinacy would do, fairly obviously, would be to demonstrate to the world how impervious I am to fact and would suggest that I consider the error essential and integral to my argument - an admission that my own opinion might be changed if truth were admitted. It should go without saying, but I will mention anyway, that the same thing would apply if I continually asserted, against all evidence, that Mr. Rogers had been a correspondent for a newspaper.
It would be an additional irony if my dependence on false authority were part of an argument against the dependence on authority, but I will let others decide whether such a strange beast is afoot here.