I believe the movie guys obtain whatever firearms that they need for their projects through special equipment rental companies. These companies are more in resemblance to armed private security contractors than a regular support company for a movie studio. They have to abide by all NFA paperwork, keep logbooks, and are subject to constant government audits. Think Knob Creek, without the actual firing range. They have personnel that are present at all movie shoots that have rented weapons from them, to make sure they are used properly and the guns don't suddenly go missing...
Before Bannerman and Sons went bankrupt and sold off all their assets in the 1990's, they were one of the No. 1 American contracts for movie and TV production firearms. At one point, their warehouse contained everything from Kentucky rifles and Springfield Trapdoors to M1 Garands, grease-guns, Tommy guns and even some crew served automatics and anti-tank cannons. Almost all of the great cowboy-western movies produced in the Golden Age of the horse opera, and popular police TV dramas like The Lineup, used firearms rented from Bannerman's.