The actual PATS module is in the column. But I don't think that is how the remote start bypasses that feature. That logic would be in the remote start module. It use to be when a remote start was installed with a system with a transponder key there was a small black box they would actually put a transponder key in that fit up under the dash. That was the way they bypassed it. Some still need that but technology has improved. Take one of your transponder keys and tape it to the column right by the key cylinder. Then get out of the vehicle and with everything secure see if it will remote start.
You need to find out how Ford does the bypass for a transponder system when you have a remote start. Somewhere, somehow there is "something" that is activated that allows the remote start to work without a key in the ignition. I wish I knew, but I don't.
The same thing is happening to me! I just bought the truck two months ago. 2006 F150 King Ranch. It didn't come with a remote so I bought one yesterday at the dealer and programmed it myself. I tried it with the key next to the ignition and now it starts! I hope somebody figures this one out! Otherwise I might buy a cheap PATS key on amazon for like $5-$10 and program it and break the chip out and tape it inside my colomn. Easy fix in my mind.
I just had a remote start put in my wife's car. They needed a chipped key to put in the system so it would work. I had two already so I bought a 3rd and programmed it so in the end we still had two. What they do is fit it in a special box under the dash that is wired into the remote start module that feeds that value in to the computer when the remote start system is activated. I asked them how a OEM remote start works without doing that. What he said was the transponder code is inherent within the remote start module from the factory. It is "married" to that computer just like your cluster is. He said it is common for that module to sometimes lose that value....hence the no run condition. In order to "fix" that a new module needs to be installed and the computer flashed to accept it.....big $$$. Just as you said, he claims you can pull the cowl and tape a chipped key inside on the right side by the cylinder. Problem is you lose your security and any key made that will turn the cylinder will start the truck.
This is all info. I was given, it makes sense, but I can not verify how this may effect other "things".