This daf continues discussing whether Bais Shammai followed their own teachings after the bas kol declaring that the halacha follows Bais Hillel due to their humility.
Once, a grandson of the Ahavas Chaim of Vizhnitz spent time with his illustrious grandfather. The grandson was a talmid chochom in his own right and served as a community rov and posek. When it came time for lunch, the grandson naturally stayed. He went to wash his hands and was appalled when he saw that his venerable grandfather had brought him a towel. Not wanting for the rebbe—one of the most respected personages of his time—to serve him, he indicated that he didn’t want to take the towel.
The cryptic reply the rebbe offered puzzled his grandson: “But doesn’t the halacha follow Bais Shammai?”
During the meal, when he asked the rebbe what he had meant, the rebbe turned to Brachos 52 and pointed to the Mishnah there. When the grandson looked at this Mishnah, he was astounded. It records a dispute between Bais Shammai and Bais Hillel as to whether one may use a shamash who is an ignoramus. Bais Shammai permits, while Bais Hillel forbids.
“The halacha follows Bais Shammai, so you could have taken the towel from me after all…” (Zichron Yisroel, p. 56)