Well not under federal law. The same rules apply gun show or no gun, it's true. But that means non dealers can sell at a gun show without conducting a background check. I've bought a couple that way, and others where the seller *was* a licensed dealer, and so I had to do the background check thing. Of course now I don't undergo the background check regardless, because I have a Texas CHL which exempts one from having to do the background check. Many other states' CHL/CCP qualify as well. But not all. It depends on whether the permit/license requires a background check.
I too have a CWP from Texas, and its good in 32 states. They still did a check at the Tulsa Gun Show on a purchase there, but it only took 20 minutes. Perhaps because it was from a Texas CWP??