I had my first PITA check-in with Southwest this year coming back from Area 1 in Phoenix, AZ. My buddies checked in next to me and went through with their guns without a problem while my Southwest person wanted me to take my gun out of the case and show her that it was unloaded. There were a lot of people around me. As I unlocked my case, and the debate continued, I asked her to call her supervisor. It took a while to get this resolved and she was not too happy that I said she was wrong.
The last thing I wanted to do was to pull out a gun, rack the slide to show it was empty. Also bring a copy of the TSA rules with you.