All of these examples of yours are properly using quotes around "client list" because the interviewer asked her about the "client list" and she responded with "It ...". Like
@FatPhil said, that's how pronouns work. And that's also how journalism works so saying
is, in fact, objectively incorrect. You can even see this demonstrated in the second link (from House.gov) using "[Epstein's client list] is ..." because "it" refers to the "client list".
This one is particularly confusing because that's the textbook definition of how to use [ ] to replace a pronoun with its antecedent to clarify the subject.
External Quote:
Using Brackets
Sometimes information is missing or inaccurate in a quote. Words can be added or changed to a quote by using brackets. Changes can be used to correct tense or to add necessary information. Brackets can also be used to make the pronouns in a quote consistent. However, brackets should not be used to change the meaning of the quote.
Brackets for Pronoun Consistency
Nathan said, "I want people to understand me."
Nathan said that he wants people "to understand [him]."
In this example, the pronoun is changed so it is consistent with the rest of the sentence.
https://www.unr.edu/writing-speaking-center/writing-speaking-resources/mla-quotation-punctuation#:~:text=Brackets can also be used,the meaning of the quote.
The Daily Beast article isn't even presenting a quote.
The single quotes around Sitting on My Desk indicate those are her actual words. The rest of the title is a
summary of what the article will say, hence the lack of quotes around the sentence as a whole. The link from the Hill even shows her full quote "It's sitting ...". KOMO and the last Yahoo link don't put quotes around "client list" at all.
You would have a valid point if any of these articles wrote
but none of them did that.
While it's possible Bondi meant something like "The Epstein case file is sitting on my desk" and misspoke, all of the above are valid ways to present what she actually said in the context of the conversation. What else would "it" refer to other than the noun in the question she's answering? Criticizing the media in this case is bizarre.