The ID instruction for me was one ID from a selection of government issued IDs. I brought what was asked for. Weirdly, they also accepted a US passport where the address is written in pencil, by the holder!
Strange, we received different instructions. For me, item 8d in your link was a 2-page document that explained the need for separate address verification if the photo ID had the wrong address.
Yeah, my photo ID had the right address because I had affixed a badge mailed to me from the DMV to the new address with the correct new address printed on it. It's a legal requirement to have the badge affixed to the driver's license after 30 days from the move date.
I think if I had attempted to apply for this service at my old address, it would not have been a problem. I applied for this service around the 30 - 45 day mark after my move. I suspect the post office may be incorporating their historic data (which includes my old address) or possibly they are integrating their mailing system with DMV data (which may itself be out of date due to timing issues in data integration).
http://faq.usps.com/documents/Informed_Delivery_Sign_Up_Guid...
Visiting the post office was easy. Getting them to accept my ID document was not.