UPDATE
I called support and they agreed that the "iPhone needs repairs" screen was "not good" and they made the appointment for me at an Apple Store. Because I had an appointment and an existing case number, the appointment took less than 10 minutes. I brought all of the packaging, accessories, receipt and my sim card still in the phone assuming they would test the phone. They seemed to be ready for me; they just swapped out my sim card into a new phone, which was activated and could make and receive calls immediately. I got a receipt for a credit and a purchase, net $0 (even though I originally bought my phone at an AT&T store). Overall, very smooth!