Barbara Branden's discussion of Rand's relationship with philosophy professor John Hospers is four paragraphs on pages 323-324 of PAR.
In paragraph 1, Branden talks of their first meeting. Hospers said that Rand had a "tremendously powerful intellect." (p. 323.)
In paragraph 2, Branden says that they soon became friends and had many lengthy philosophical conversations. They agreed on moral and political philosophy, but not epistemology. Hospers recalled that their arguments became heated at times and that Rand easily grew angry. Hospers describes her "sudden anger" as "bewildering." (p. 323-324.)
In paragraph 3, Branden says that Rand "broke" with Hospers. In 1962 Hospers invited Rand to speak at an academic symposium and Hospers criticized some of Rand's presentation. "Ayn took violent exception to his criticisms--and he never saw her again." (p. 324.)
In paragraph 4, Branden writes that Rand's relationship with a professional philosopher "made her eager to write a nonfiction work on epistemology." (p. 324.)
Here is Valliant: "Professor John Hospers, according to the Brandens, was taken to task for certain 'sarcastic' and 'professorial' criticisms of Rand in an academic setting, although, once again, neither of the Brandens chooses to relate the specifics." (PARC, p. 71.) Valliant drops a footnote and references both PAR and Nathaniel Branden's Judgment Day. Nathaniel Branden says Hospers "challenged her viewpoint with the kind of gentle sarcasm professors take for granted." Barbara Branden does not use similar words to describe Hospers' comments. Valliant should not present the two accounts as if they were one.
In any event, Nathaniel Branden appears to believe that Hospers' tone was liable to be misunderstood. (Judgment Day, p. 307-8.) Barabara Branden appears to think that Hospers' comments were appropriate to the forum and Rand overreacted. There is a minor discrepancy over Hospers' tone, but other than that what is the big dispute here? Although neither is happy that there was a break, they both concede that epistemology was an area of dispute between the two philosophers and neither states (contra Valliant's implication) that philosophical disagreements shouldn't be cause for "moral indignation." And even if they do believe this (which they don't express in the context of this break) I don't see how it lessens their credibility.
According to Nathaniel Branden, Rand directed him to read the "riot act" to Hospers. Valliant is upset that there is no description by either Hospers or Nathaniel Branden of what the "riot act" consisted of. He ends his discussion with a claim that there are "missing details." Personally, I am satisfied that after the passage of roughly 25 years (from the time of the event until the two books) that we know basically what happened.
Incidentally, neither of the Brandens describes the split as an "excommunication" as Valliant calls it or indicates that Rand demanded philosophical loyalty from Hospers.