DL sticker won't work because it's not "issued by the state". However, the correct address info/documents they won't accept, including your word, are accepted by any retailer (at least in my experience) for something like an extra rod license. So you can't say, "this is my correct address" to the FFL, but you can then say that to the gum snapping chick at the Sportsman's Warehouse licensing counter and then all is well. Makes no sense.

Similar and equally stupid:

I have DV plates on one vehicle. Recently got a different vehicle and went to the DMV to get it registered. I asked if I could pay the extra to get DV plates on that vehicle as well (free parking/entrance at state parks, which is handy for the Cheyenne Mountain State Park Archery range). Sure. Just need the DD214 and VA letter. But... every year they send me a new registration for the vehicle I already have the DV plates for, without those documents, and I showed them when I got the plates originally. Nope. Every. Single. Time. you want to get DV plates for a different vehicle you have to show those documents. But yet they just renew the current ones for the original vehicle no questions asked. Sense level: government.