RSYK also told me that he heard from RYG of Edison that with this Gaon, the passuk by Yosef (45:13), where he told his brothers to let their father know of his great כבוד in Mitzrayim, he wasn't telling his father how wealthy he was, he was telling his father that he remained loyal to the Torah. It says והגדתם לאבי את כל כבודי במצרים, Kavod Malei, that he was still thinking about the sugya of Egla Arufa.
In the comments, you will see that this "rule" appears to be correct around 50% of the time, in other words, a random distribution. If it were intended homiletically, I wouldn't mind, but when the Chafetz Chaim brings such a thing from the Gaon, it is intended to be 100% correct and not just homiletics. It is possible that the Gaon holds that all our Tanachs should be edited to conform to this rule. Otherwise, I just don't know what to do with this. I'm waiting for an explanation. In the comments, I quote Rav Amar, who claims to have a way to make the pshat work. I also am putting it here, at the end of the post, in small letters.
Ari Levine, in a comment, directs us to an excellent source. He says that Rav Zvi Ron showed him the question and the answer attributed to the Gaon in the Medrash Sechel Tov (compiled five hundred years before the Gaon), and it is on our parsha, here.
This is what the Medrash Seichel Tov says:
As I mentioned earlier, Rav Amar talks about this question in two places that I found, as follows.
In the first case, he brings that someone used the Gaon to explain Yosef's message to his father, as I noted in the post.