If they denied registration based on color, then the color was not allowed.
Some registries did do that. Still do? Basically casting aspersions on the authenticity of a foal’s pedigree, as stated by the owner.
However you are correct that owners of purebreds are often only able to see colors that are allowed by the registry. So all of their horses are one of those colors, because the owner doesn’t acknowledge any other possibility.
But that does not change the fact that many color-restricted breeds do have more color than they are willing to admit exists in the breed. Color is still seen by some as a hallmark of a purebred, even though scientifically that is not accurate. I know some people who will never give up that opinion (“knowledge”, in their lexicon).
We won’t even get into the black dots that appear on some horses, but aren’t there in the eyes of people doing registration descriptions.
From childhood onward, I have been schooled more than once by friends not to remark on interesting points of color on their horses or other horses at their favorite shows!