The reason for this is because it seems that film prints didn’t actually look that, and the green tint slathered all over the image most likely actually was only added for home video. During the production itself, the main methods by which the unreality of the Matrix was emphasized visually was through bleaching out the sky to eliminate as much blue from it as they possibly could, creating unusual contrast through lighting on set, and sometimes using green filters in-camera and in the color timing. On film, this is evident because some of the Matrix scenes do look somewhat greenish, but not all of them, and not nearly to the extent that they do on video. The DVD already diverges from the original look to a considerable extent, and the Bluray is particularly revisionist (in a nasty, ‘digital’ sort of way), and looks nothing like the film version.