Q. There is a famous story where the Chofetz Chaim tells Rav Shimon Schwab that he is a Kohen while Rav Schwab is not because when Moshe Rabbeinu called out “Mi Lashem Eilai”, his father answered the call, while Rav Schwab’s did not. And therefore, when he hears the call, he should come running.

I have two difficulties with this story.

1) Those who came running did not become Kohanim. They became Leviim. Not everyone who ran became a Kohen. Aharon HaKohen became a Kohen because Moshe Rabbeinu lost the Kehunah and Aharon was glad over his brother’s appointment as the leader of Bnei Yisroel. So the running had little to do with it. Additionally, the Leviim became Leviim because they were free of involvement with the Eigel and demonstrated their allegiance. Aharon was involved in the Eigel, and he still became the father of the Kohanim.

2) Rav Schwab could have retorted, “No, my ancestor may have run as fast as yours did, but what could I do, somewhere between him and I, we had a grandfather who only had daughters.”

A. There are a number of seforim that quote this story (Ma’adanei Shmuel – Emor p. 327, Likutei Chofetz Chaim – p. 168, Vezorach Hashemesh p. 333, Cheshbonos Rabim p. 92, Talelei Oros – Ki Tissa, Hasimcha Hoamitis p.202, to mention some). One, however, Reshimos Mehava’ad (p. 140), mentions that the Chofetz Chaim asked Rav Shwab “Are to a Cohen or a Levi? This could be the true version of the story.
The most likely answer is that often Cohanim and Leviim titles were used interchangeably (Devarim 24: 18 et. al.).Rashi, (Shemos 32: 29) actually mentions that the responders will become becoming Cohanim at the initiation act of the Leviim responding to Moishe’s call.
Indeed, Rashi (Devarim 10: 8) writes; “At that time: During the first year of your departure from Egypt, when you erred (by making) the calf, and the sons of Levi did not thus err, Hashem separated them from you.” The process of not erring involved also responding to “Mi L’Hashem eilai”
Horav Shlomo Miller Shlit”a explained that the gift of being a Cohen or a Levy was granted for all generations to the responders of Moishe’s call. Whether due to any individual and unique circumstances, some ended up using it or not, does not negate that the recognition was given, and the responders became Cohanim-Leviim or at least have ancestors that did.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a