Just based on your careful description, here's my guess.
You've noticed that two of the 3 beams are indeed linearly polarized, oppositely. (If circular polarizations had been used, the blocked beam wouldn't have been sensitive to rotating the lens.) Now when those beams bounce off the screen, quite a bit of the polarization is lost. Thus when you look through the rotated lenses, nothing completely goes away when you look at the screen.
There should be enough polarization left for the intensity of the images to be significantly different through the different polarizers,
So far that wasn't guess. Here's the guess part. Maybe the brain then uses that intensity difference to construct a 3-D image.
Mike W.
(published on 02/01/2010)