Well no. You could go out tomorrow and make your own movie of Snow white, or Beauty and the Beast or some other public domain story, and many people have. What Disney work so hard to do is prevent its particular versions of various from falling into the public domain. Now I think they're missing a trick insofar as they would still be able to sell Official Disney Versions even if their famous animated movies went into the public domain tomorrow, because they have the best marketing operation on the planet (so kids would demand 'the real one') and they could keep adding more content (eg additional 'making of' documentaries and so other extra features that serious fans of a film will pay to watch).
I'm in broad agreement with you, I just want to be clear that when Disney makes a film out of a folk tale or so it is not claiming property rights over the source material, just the firm's own rendering of it.