I've flown with guns recently. No problems, as stated above.
The >>latest<< TSA policies delete the need to prove to somebody that the gun is unloaded. Instead, you declare both verbally and in writing that it is, and a tag with your declaration goes into the sealed luggage with the gun, face up and on top. It's a red or orange tag with big black letters "DECLARED FIREARM" or something like that. I assume it can be picked up on X-Ray.
So far I'm not aware of these tags being used by criminals within TSA as "steal me markers". My guns haven't been messes with across several trips now, and I'm not aware of reports of theft. So they've got a decent, working system in place.
That "declaration system" is probably how SouthWest handles it now, and the site linked discussing inspections is outdated.
WARNING: under the "declaration system", you're stating UNDER OATH that your bangthing is unloaded. God help you if it ain't. M'kay?
Also: the SW air site linked above says something about knowing the gun laws at your origin, destination and points between. Whoever wrote it is probably not familiar with the Firearm Owner's Protection Act, a Federal law as of '86 that protects "passers through". If you're coming from AZ headed to OH by way of Chicago, Mayor Daley and his minions can't hassle you. NYC was infamous for this sort of thing for a while but have lost a couple of cases based on FOPA and last I heard had stopped trying to subject those headed on to Vermont or whatever to NYC gun control. This applies even if they're landing in NYC by plane and driving on to VT, NH or the like.