The email exchange, which took place last July, involved the show's executive producer Henry Louis Gates Jr and Sony Pictures co-chair Michael Lynton.
In the leaked messages, Gates asked Lynton how he should handle Affleck's request, in which the 'Gone Girl' star asked that the docu-series withhold the information about his slave-owning ancestor.
"Here's my dilemma. Confidentially, for the first time, one of our guests has asked us to edit out something about one of his ancestors--the fact that he owned slaves. We've never had anyone ever try to censor or edit what we found. He's a megastar. What do we do?," Gates wrote.
Gates replied, "It would embarrass him and compromise our integrity. I think he is getting very bad advice. Once we open the door to censorship, we lose control of the brand."
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Affleck's name is not mentioned in the email exchange but the actor is referred as "Batman" and "a megstar."
The episode on Affleck focused on the actor's mom, who was a "freedom rider" in the 1960s but there was no mention about the ancestor who owned slaves.
PBS posted a statement on its website saying: "It is clear from the exchange how seriously Professor Gates takes editorial integrity.