After about 15 minutes, the main supervisor, Laurie, arrived. Again, Laurie was exceedingly nice and professional, but seemed a little more concerned than Brenda. She asked if I was sure I didn't have photo ID, like a credit card with my picture on it, or even a CostCo card. I wound up going through my wallet in front of her to show that I didn't, and she pointed to various cards and receipts in it to ask if they were IDs. I wound up showing her everything to prove I was telling the truth. She repeatedly said they had no way of "verifying" that I was who I said I was, and that someone could have stolen my credit card and traveled under my name. I didn't want to mention that they shouldn't need to verify who I am, because I was afraid they could then say I wasn't cooperating and deny travel on that ground. In fact, I even mentioned several times that I wanted to fully cooperate with them because I was aware that was a component of the new regulation, and they assured me that I was.Link (Thanks, Meg!)
Finally satisfied that I didn't have ID, Laurie took my boarding pass and went away. She came back a few minutes later having photocopied it, and also had an affidavit that she requested I sign. It asked for my name and address, and stated in small print at the bottom that I did not have to fill it out, but if I didn't I couldn't fly. It also said that if I choose to fill it out and then provided false info, I would be in violation of federal law.