My guess would be that door example is either an amature, or an old pro job.. looks like the vinyl on the top left (by the window crank) and the bottom right is comming up.. as evidenced by the wrinkles.
All in all, tho.. I really like the way it looks.. it's obviously not stock, but it has a very clean retro feel to it.. i'll bet the average person without any real knoledge of old cars & trucks would know that wasn't stock.
I was watching one of those hot rod/resto shows a few years back and this guy was doing the door panels for the project.. he didn't use a single stitch.. all the fabric and material was put on with glue.
The guy cut this thin board.. little thicker than paneling, and thinner than plywood to the shape of the door.. for the 'groves' you see in the top part, he cut shallow lines in the wood with a saw.
Then he rolled on some kind of contact cement/glue stuff.. looked like the stuff you'd use to put linolium down with.. he rolled the glue on the length of the backing board a strip or two at a time, then laid down the vinyl, using the handle end of a butter knife to get the vinyl into the 'groove' and used a roller thing to press down the 'flat' parts.
The key, he said, was not to try and glue it all in one shot.. to do one or two 'strips' at a time. Once he got all the 'striped' area done, then he cut the excess from around the edges of the board and folded it back, using the same glue to secure it.
The bottom section went on the same way.. but without the hassle of the 'strips'.
When I get closer to doing the door panels in my Galaxie, i'm going to get some small, like 1 foot square pieces of wood and fabric and experiment with that method.. but it really seems like the toughest part of the whole process would be to get those lines cut straight and uniform.. the gluing the stuff down part outta be a piece of cake.. since the pattern is actually in the backing board, you don't even really need to glue the material down straight! (unless the material is going to have a pattern or something on it.. which would probably look stupid with horizontal lines going across it!