Leonard Peikoff in My Thirty Years With Ayn Rand: An Intellectual Memoir (epilogue of The Voice of Reason), talking (after her death) about conversations he had with Ayn Rand:
“You are suffering the fate of a genius trapped in a rotten culture,” I would begin. “My distinctive attribute,” she would retort, “is not genius, but intellectual honesty.” “That is part of it,” I would concede, “but after all I am intellectually honest, too, and it doesn’t make me the kind of epochal mind who can write Atlas Shrugged or discover Objectivism.”
I think the answer to this is simple: Peikoff should not assume that he's intellectually honest. He should take seriously that maybe Ayn Rand is right and that superior honesty sets her apart. It was dishonest of Peikoff not to consider that he might be dishonest compared to Rand. He might not even be aware of some of the ways she's honest that he isn't. He might not know about some types of honesty and how to judge whether he has them. He also might not know about some types of bias or dishonesty, and how to accurately judge whether he has them (it's common to be dishonest when evaluating your own honesty).
Soon after, Peikoff writes something relevant:
In order to be fully clear at this point, I want to make one more comment about Ayn Rand’s anger. Many times, as I have explained, it was thoroughly justified. But sometimes it was not justified. For instance, Ayn Rand not infrequently became angry at me over some philosophical statement I made that seemed for the moment to ally me with one of the intellectual movements she was fighting. On many such occasions, of course, she remained calm because she understood the cause of my statement : that I still had a great deal to learn. But other times she did not; she did not grasp fully the gulf that separates the historic master, to whom the truth is obvious, from the merely intelligent student. Since her mind immediately integrated a remark to the fundamentals it presupposes, she would project at once, almost automatically, the full, horrendous meaning of what I had uttered, and then she would be shocked at me. Once I explained that I had not understood the issue at all, her anger melted and she became intent on clarifying the truth for me. The anger she felt on such occasions was mistaken, but it was not irrational. Its root was her failure to appreciate her own intellectual uniqueness.
I don't think this account is fully honest. Peikoff isn't very self-aware. He should have taken more seriously that Rand's intuitions could be correct. Maybe she was getting angry for a reason. In other words, maybe Peikoff was doing something wrong. He could have considered that more. There are signs in both of these passages that he wasn't actually very deferential or respectful to Rand's judgment. He'd disagree with her and expect to be right, even though he won zero or near-zero debates with her.
Here's what I think Peikoff was doing wrong: he (on multiple occasions) made horrendous statements without knowing what he was talking about. That's not just an unavoidable accident. He could have asked questions or made more tentative or conditional statements. He could have spoken within the limits of his knowledge instead of trying to make claims about issues he didn't understand at all.
I actually talked about that in my essay on lying. See e.g. the section "If You Don’t Know, Say So" or in the section "Reasonable Expectations" where I wrote:
Communicating that you know more than you actually know is lying. If you speak confidently when you don’t know what you’re talking about, you’re being dishonest. An honest person makes his words and tone match his thinking.
I don't think getting angry was the ideal reaction from Rand. (I'm not confident that Peikoff understood Rand's emotional states accurately, so I don't know if she really was angry.) But Peikoff was no innocent. Based on his own story, she was reacting negatively to him doing something wrong. And he still doesn't know what he did. And he doesn't respect Rand enough to assume that if she was angry then he did something bad that he shouldn't recount to the public (I don't think he wants to share his flaws, look bad, and tell Objectivists specifically about how his flaws and mistreatment of Rand drove her to anger).