Would you say that once a film is released, the filmmaker no lomger "owns" the message of the movie?

I've always been fascinated by the idea that once a film is shown to an audience, the filmmaker no longer "owns" the message of the movie, but rather the audience takes over with its own interpretations and beliefs in the themes and meanings. The views of this matter in Hollywood seem to be split. For example, The Wachowskis refused to do press junkets for the Matrix films because they wanted the "films to speak for themselves" and felt that by explaining their intent it would devalue the importance of the audience's interpetration. Then on the other side of the coin there's George Lucas who "can't let sleeping dogs lie" as Spielberg said. His retooling of the Star Wars films has been indicative of this. Spielberg himself seems to have changed his views and said he regrets having updated ET because the film was "no longer his" after the theatrical release.

So is the movie yours once you see it? Or does the filmmaker's vision trump your own opinions?

I would like to get the opinions from a broad range of viewers, and I will also be asking this question of r/filmmakers. Thanks very much!