Rashi mentions that when the Israelites were required to ascertain their lineage to join their respective tribe, this document was brought in tandem with the testimony of witnesses.
In its place, kohanic legitimacy was determined based on the presumption, as well as the absence of a disqualifying objection by two witnesses in Beit Din.
[4] To summarize: according to Rabbi Yossi, a close reading of the disqualification narrative reveals that the family actually remained qualified to perform certain priestly actions based on their historical behavior.
The author of Avodah Tamma asserts that they were known to be descended from Aaron, but the suspicion was that one of their ancestors had engaged in a forbidden marriage, and thus disqualified from the priesthood as challalim.
The Talmud Yerushalmi explains that Barzilai himself was a Jew, but his daughters were born non-Jewish and converted to Judaism before being three years of age, making their marriage to kohanim forbidden by rabbinic law.
Leading Rabbinic authorities, such as Joseph Trani and Samuel Ashkenazi, disputed reliance on the Isaac ben Sheshet's response for purpose of questioning the authenticity of the kohen.
[19][20] Rabbi Samuel de Medina, in a response concerning a woman who was held captive as a young girl, ruled that a kohen is permitted to marry her.
[21] This responsum of Samuel de Medina was met with a fiery reply from Ezekiel Katzenellenbogen: I have seen in some responsa and have also heard (about) a few Rabbi's who seek to be lenient regarding today's kohen and label them as "uncertain", I forbid myself from agreeing with them.
Since they were already rebuked with one hundred (lashes from) metal-tipped whips from the hands of reputable rabbis making the issue forgotten to expose a falsehood on the authenticity of the Kohanim..let me not be with those responsa, not even as a sidebar to their opinion.
[19] As proof they cite another responsa of Samuel's, where he prohibits a presumptive kohen from remaining married after her possible but not certain receipt of a bill of divorce.
On the one hand, he argues that herem intended for priests (whether land or goods),[24] as well as shoulder, cheeks and maw,[25] should be given to a presumptive kohen.
However, he also legitimizes the questioning of priests' legitimacy following the Khmelnytsky Uprising, writing that this and similar upheavals utterly confused the lineage tracking of persecuted European Jews.
[24] Luria quotes a story in which Hai Gaon would travel to Jerusalem for Sukkot and circle the Temple Mount with hundreds of kohanim in the company of Elijah the Prophet.
[34] A more extreme approach was taken by Chaim Hezekiah Medini who exclaimed, amongst a group of arguments, that Emden's advice created a cloud of uncertainty and doubt as to the otherwise legitimate lineage of the modern kohen.