Crazy. I'm assuming your in Kentucky? From what i read about indiana parts for filings, a social security number is required. Wonder how that works for that part. Need all the ffl dealers to chime in if they experienced this before..I did a firearm transfer for a non resident alien a few years back. My first reaction when the guy inquired about it was the same as yours, but I did some checking and yep, sure enough.
There was at least one extra form that had to be completed and attached to the standard 4473, and the non citizen had to show proof of something or other that a US citizen doesn’t have to show, but aside from that, it wasn’t a crazy process.