No, greens are not created by crossing reds with albinos.
The genetics of color in complex paphs is pretty complicated.
Paphs (and other types of orchids) express 3 types of color pigments:
anthocyanins - reds/browns/purples
carotenoids - yellows
chlorophylls - greens
The color and pattern of a bloom are a result of the combination of those 3 pigments.
In an 'albino' orchid, there is no expression of the anthocyanins in the blooms or leaves. This is why you get blooms that are a mix of green, white, and yellow. Any purple spotting on the leaves will be absent in an albino.
There is no such thing as an orchid that lacks carotenoids and chlorophylls. Both of these pigments, in addition to providing flower color, perform vital functions in plant metabolism. A plant without them wouldn't be able to grow.
Complex greens and yellows have albinos in their backgrounds - which is where the lack of expression of anthocyanins come from. But pure whites will also have albinos in their background. So that begs the question - why are some albinos white, some green, some yellow? That all comes down to the genetics of carotenoid/chlorophyll color expression & suppression in the blooms. Some species (e.g. a lot of the brachys) suppress virtually all carotenoid/chlorophyll expression in their blooms, leading to a flower with a pure white background. As such, the brachys play an important role in the background of white flowers.
So why do they keep breeding whites with greens in the hopes of getting big clear whites? Because each has a property the breeder wants: He wants the clear white color from the white and the size from the green (greens are some of the largest of the current complex hybrids). The hope is that some of the seedlings will inherit the large size from the greens and the ability to suppress carotenoid/chlorophyll expression from the white.
There is a lot more nuance to color development than what I've listed here. There is sometimes partial albinism in flowers and variations in the levels of color expression. This is especially true when a hybrid is 10+ generations removed from the original species.
--Stephen