I called them back 800-479-5981, press option 3, and speak to Jenny. Explained that I signed up last week, and that I registered a VISA and my Diners Club, but that others had told me that AAdvantage Dining can't do Diners, she told me emphatically that YES, DINERS IS ELIGIBLE.
I can't vouch for it, as I haven't used it, and likely won't anytime soon, as this is my biz travel card, and I don't have any trips scheduled at present, but I have gotten the same answer from the 2 folks I spoke with, so I'd suggest if you have a question, call them and ask.
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Celebrating 4 years of United Airlines free travel this August!