It's all about the context. And keep in mind that how the information was consumed in the original context may be different than how it will be consumed by a random Googler who makes his/her way to J.SE.
(There is a crucial disagreement, by the way, as to whether lashon hara applies to the deceased. The Chofetz Chaim prohibits it, but many, many others, including R' Yaakov Kaminetsky, say the prohibition is only on libel: a historian has carte blanche with true material about those no longer with us. Beyond that, nuance in lashon hara is tricky; as a historian, Rabbi Rakeffet himself has said he felt it would be appropriate to write in a biography of someone deceased that, for example, Mr. so-and-so was so emotionally invested in the success of the yeshiva that its financial troubles sadly led him to a drinking problem -- the goal isn't to denigrate, and it's explained in context.)
The story referenced here is, at first glance, not unlike one in the Talmud:
A convert offered to convert to Judaism but only on some silly conditions; Shammai chased him out the door with a stick, but Hillel worked with him. We are explaining that a complex situation will be seen differently by different great people; and that their halachic viewpoints may stem from different personalities and angles. Often a balance is needed -- to quite Rabbi Berel Wein, "a Judaism without Shammai has no spine, while one without Hillel has no heart."
Rabbi Rakeffet is a historian training rabbis and educators. He wants them to understand different personalities of the past generation and how that affects the Jewish world they'll encounter today. In that context, it was useful to know which rabbis insisted on "spine", and how that informs other teachings or students of theirs they may encounter.
A very similar episode occurred on a yahrtzeit of the Brisker Rov, R' Yitzchak Zev Soloveitchik. Rabbi Yosef Dov Soloveitchik sermonized that one great rabbi 1950s Israel, Rabbi "A", was willing to sit and negotiate with David Ben Gurion, but his uncle the Brisker Rov was so "pure Torah-only" that he didn't do so. One of the listeners was incensed that anyone attack Rabbi "A" like that, and began screaming back in the middle of the sermon! This was, again, misunderstood based on context: Rabbi Yosef Dov himself was unafraid to get involved with all sorts of complex figures when the cause was right (including Catholic clergy to help the State of Israel); he wasn't saying Rabbi "A" was bad or wrong; just that it highlighted the complexity of the question and the way his uncle had a different approach.
(Notice how I'm omitting names there because it would just distract from the point at-hand.)
Getting back to J.SE: it depends on the context of the question and the answer. In the context linked, i.e. just answering the particular halachic technical question, mentioning which rabbis were flummoxed is probably distracting. (And if that's the first thing that shows up when someone Googles that rabbi's name ... probably not ideal, especially as it doesn't help answer the question here.) I'd likely say -- [one great rabbi] was flummoxed by the student's defiant snark, but I thought it was an opportunity to give a classical answer and engage them. With a link to the relevant recording so that someone who wants to do more research can follow it from there.