It's a pretty common problem with trailers having a plug that isn't made to the exact specifications in diameter, so the plug fits loose in the truck's OEM receptacle.
I hear about a lot on GM truck forums. I experienced it myself too. I had never heard of the problem until I was describing my symptoms to the dealer I bought a cargo trailer from. He explained it and some some brands of trailer pigtail plugs fit loose in OEM receptacles.
I changed the pigtail, problem solved. That was about 3 years ago, and I've never gotten the "check trailer wiring" on the DIC again.