They sure do. First time was at one of the Federal Agencies who were in the same Federal Bldg. where I worked.
Second time was by the local Sheriff. They had a guy who clearly knew what he was doing so I know they had a good set.
The third time, I just ignored the request. By that time I decided it was just their was of trying to make me nervous.
I do remember several years later I decided to look at my personnel records. I was pleasantly surprised at what good interviews they had given on me. Two, one a Sergeant at Lackland and another at a Summer retreat had literally said I was the best they had ever had.
Then I got to wondering. They had interviewed every person I had ever had close ties to including former neighbors. Then I realized a former boss was not in the file. I actually liked him OK but another worker once told me he was furious at me for questioning something he once said.
They remove any derogatory info after I think 3 years. That had to be it but I have no idea what he told them.
I never had to submit fingerprints to purchase a gun. They just call a number and that’s it. Takes less than five minutes.