midrash - How do we know that Zimri was the same person as Shlumiel ben Tzurishaddai?

Sanhedrin 82b says that Zimri is the same person as Shlumiel ben Tzurishaddai, and that Zimri is simply a derogatory nickname. But in the passuk that identifies him, he is described as "נשיא בית אב לשמעוני" - a head of a household from the tribe of Shimon. But in Bamidbar (4:38), when Hashem commands Moshe to count the descendants of Kehas, it says "נשא את־ראש בני קהת מתוך בני לוי למשפחתם לבית אבתם". So how do we know that Zimri was not simply the head of a family and not the head of the entire tribe?

(Note: Zimri's being the head of a family within the tribe does not disqualify him from being Shlumiel ben Tzurishaddai, since Zimri/Shlumiel could have been both the head of a family and of the tribe as a whole.)