I want to rephrase my statement: as a rule, local theaters don’t decide.
I have no doubt that there are still some little mom & pop theaters somewhere that personally choose their trailers to match their upcoming selections. But insisting that this is The Way It Is Done is as wrong as saying that grocery stores still hand-price their stock or gas stations still clean your windshield and check your oil.
Can you give me a citation showing that there are theaters which show trailers of films which they won’t be showing? This sounds really strange to me. I’ll concede that there is one such circumstance. XYZ Corporation might own five different movie houses around a big city (and its suburbs) with a total of 24 screens. They might show trailers for movies showing at the XYZ A Boulevard Theater at the XYZ B Hills Theater (with a note that the film is only at the A Boulevard Theater). That’s because it could make money for them to encourage customers at the XYZ B Hills Theater to come to the XYZ A Boulevard Theater occasionally for some movies. It makes no sense though for W theater in small town M with one screen to show a trailer for a movie whose closest showing is at the N Theater in city P fifty miles if the W Theater isn’t owned by the same company as the N Theater. That would be simply telling people that they needn’t bother with seeing movies at the W theater, since they can’t get anything except one movie at a time. Companies don’t deliberately do things that don’t make them money.
O.K., let me modify my previous answer. I was assuming that all the trailers for movies were selected by the management of the theater or the management of the theater chain. That’s how it works for all the theaters that I go to. However, there might be cases where the trailers for a movie are not selected by the theater or theater chain. There might be cases where the trailers are selected by the distributors of the movie, and the trailers will all be for movies distributed by the same distributor. The theater might be told by the distributor of the movie that to show the movie that they have to show the trailers. In that case, it would make sense for there to be trailers for movies that will not show in that theater or even in that theater chain, since such trailers will be making money for the distributor. I don’t know if that actually happens, and I don’t think I’ve ever seen that in any theater that I go to.