No, typically producers aren’t the primary authors of the film. Typically a director is the primary author (especially when acting as a co-writer). However in case of OT, Lucas was the primary creative director. He basically came up with the main ideas (story, characters, concepts, etc.), he co-wrote screenplay and oversaw the the rest of the writing, he worked with conceptual artists (McQuarrie, Johnston, etc.) to put his ideas into reality and worked with the editors to make the final cut. Basically the hired directors had control over principal photography, i.e. directing actors and crew to realise the scenes, which is exactly what they were hired for. In case of ROTJ Lucas was interfering with Marquands work during principal photography, which makes me wonder why he hired him in the first place.
So would this mean that JK Rowling has the right to go through the Harry Potter film series and impose changes - even changers that the directors of those films don’t agree to?