They will get your truck by trading one of their vehicles.
PS, I pick up my new F150 tomorrow
I didn't do quite what you suggested in the beginning of your post, but did end up with a "traded" vehicle.
Found my numbers, decided what my bottom line would be, made a few calls and emails, "negotiated" with a couple on the phone, with limited time to play ("Put me on hold while you go 'talk to your manager', and you'll come back to a dead line..."), then made one last call to the local guy, and told him who had beat him and by how much.
Within 10 minutes, he found the vehicle I wanted at a dealership about 1 1/2 hours away, beat the "other" best deal by a few hundred bucks, had the vehicle swapped and delivered to his dealership, and the deal was done.
It came home an hour ago.