Data point: just got denied for #5.
I called yesterday after I applied, and was told no, but decided to call again today. Before I could even say anything he was like, this is denied, but I'm a supervisor so let me see what I can do. Then after the hold he told me there was nothing he could do and that he was really sorry and made it really clear that he didn't want it to discourage me from applying for more Citi cards in the future. He said that my inquiries were below 6, but that I have 13 new accounts this year and so it was unfortunately a no for this card. I would trust what he says as a supervisor more than just the regular agents, so I'm thinking this is a pretty good indication to people that were wondering that maybe it really is new accounts more than inquiries that they will deny for.