I completely agree with everything you wrote. There are two seperate "Shelby" Mustangs. Shelby American has never been part of Ford and the "factory" Shelbys that would go on this list if they where still in production license the Shelby name from Shelby American. The Mustangs that I linked are made independently by Shelby American and go in the aftermarket/modified category with Roush and Saleen.
The GTD is made by Multimatic, the difference between the GTD and the other cars mentioned above is that the GTD is made on Fords behalf. Ford hired Multimatic to build the GTD because Multimatic also make the Mustang GT3 race cars. Multimatic also handled the manufacturing of the 2017 Ford GT supercar and many other high performance cars as you can see in the link. So if the GTD doesn't count as a Ford factory car, then neither does the GT.