This story of the Chofetz Chaim is dubious at best - not only does the Chofetz Chaim not hint to this halacha in his works, but he implies strongly to the contrary.
ודע עוד, דאפלו אם בתוך הגנות שגנה את חברו גנה את עצמו גם כן בזה
הגנות גופא, ואפלו הקדים להתרעם על עצמו בזה, אפלו הכי
מכלל דילטוריא לא נפקי
The Chofetz Chaim writes that talking against one's friend is prohibited, even when he includes himself within the slander he says about his friend. If he held it was equally forbidden to talk about oneself as one's fellow, there would be no 'אפי׳'.
But not only is this story probably inaccurate, relating this story is probably loshon horo (or motze shem ra, depending on it's veracity) - because even if it were permitted to speak degradingly about oneself, it would nevertheless be forbidden to talk about oneself in the manner he did - because the listener was not aware that it was permitted.
The Chofetz Chaim rules (Klal 6:42) that it is forbidden (under the prohibition of lifnei iver) to talk about something permitted if the listener is not aware of the situation that makes it muttar (for example, l'toeles) - since the listener thinks it is something prohibited, it classifies as 'נתכוון לאכול בשר חזיר ועלה בידו בשר טלה', which is a form of trangression. According to Tosfos (Kiddushin 31), one would not be allowed to extend Kosher meat to someone who believes it is not Kosher.
Accordingly, it would be forbidden to slander himself to a listener who is not aware of his identity.
Therefore, relating a story where the Chofetz Chaim supposedly transgressed either Loshon Hora or lifnei iver would be forbidden.