No they all don't. And I was surprised the first time I had the request. Went through with that deal. Won't do it again. It is NOT required by law. It's an arbitrary requirement some just choose to implement.
I believe they ask for the license so they can put the appropriate data in their books. I had an FFL a long time ago and I recall needing information when receiving firearms from a non-dealer, and the DDL gave me what I needed.
