John (Suds):
I think what was going on was that Ford was probably very aggressive at seeking placement of Lincolns in movies. Lincolns appear in a lot of "A" feature films of the time, including A Star is Born, where James Mason has two of them, and Picnic, where Cliff Robertson and his father both drive them. All That Heaven Allows has two as well - Jane's sedan and Conrad Nagel's hardtop coupe.
What was done to put cars in movies was that the automaker would either get a request for cars from a studio, or would meet periodically with studio people to offer cars. When a car was wanted, the automaker would build and ship precisely what was needed to an L.A. dealer, who got a great price on it. The dealer delivered the car to the studio and provided any needed service, with the automaker picking up the tab. When filming ended, the dealer got a "cream puff" used car with a great sales story - "Did you know James Mason drove this in a movie?"
Ford was so good at this kind of thing that they could handle some very special "special requests." On Alfred Hitchcock's North by Northwest, a Lincoln Mark III convertible was needed for both location shooting at Mount Rushmore and studio shots at M-G-M in Culver City, CA. No problem, said Ford. They built two identical cars, delivering one to a Rapid City, SD dealer and another to an L.A. dealer. This meant no hassles shipping a car, and no possibility of damage enroute that could hold up shooting. Onscreen, you think all the shots are of the same car.