Well, the paint genes aren't always dominant. Consider it this way. Solid paints are in essense possible hets. However it only takes one copy of the paint gene (tobiano, overo, sabino etc etc) to make a visible 'morph'. Clear as mud right?

Pretty much it comes down to you get a solid horse from a paint or two paint parents they consider that it carries paint bloodlines and thus is still allowed registration only with restrictions, you can't show in regular registry (colored horse) classes in shows and there usually are less classes offered for breedingstock/solid paint breds.

That's a very sloppy explanation though it should help.