Hey, Moosie, I'm not really takin' sides on this issue. Either party could be the bad party, and either party could also be willing to lie.
Now, as far as how "they" may find such information - I would offer a couple of possibilities. The first is that the applicant may have some kind of record accompanying the previous marriage. Again, it may or may not be legitimate (PFA's are easy to get, ya know, whether deserved or not -- again, courts err on the side of caution). The second possibility is that the subject comes up in the reference check.
Please understand, I am not vouching for any of the stories or the people. These folks are able to buy and possess weapons, so they must not have anything like a criminal history of violence. To me, assuming that you are able to possess weapons, most previous transgressions are surmountable. Things like a history of violence, substance abuse, or mental illness -- are probably not.