Are your birds first generation stock? That is to say, did you hatch them from birds your bred or buy them as eggs/adults? If they aren't first generation birds how many generations back have you kept the stock?
If they are first generation some likely had an all white parent. I'm not that informed yet on quail color genetics but I believe breeding a golden with a bird of any other color is supposed to yield a certain percentage of goldens and a certain percentage of birds of the other parents color (or other colors back in the pedigree). I have heard that golden is a terminal gene, one copy of the gene creates a golden but two copies results in fetal death, therefore good breeders mix their stock to increase hatch rate and increase the stability of future hatches.
I'm sure others have the numbers and further details on golden genetics, but I would suspect that is what is at play here. I think if your browns had whites in their lineage they would turn out tuxedos before they would have a solid white pop up.
It'd be great to see a picture if you can get one!
Cheers,
Jessie