The breeder probably WAS as strict as she thought, and the white rooster IS pure white.
When you cross a white chicken (two copies of the recessive white gene) to another white chicken (two copies of the recessive white gene), every chick will also be white (two copies of the recessive white gene.)
So you can breed pure white chickens forever, (like the breeder was doing.)
But those chickens still have genes for blue or not-blue, and for gold or silver, and for barred or not-barred, and for partridge or solid black or some other pattern, and so on. You do not see any effects from these other genes, because the chicken is all white, but they still have all those other genes. It's as if you took a colored chicken and dipped it in a bucket of whitewash.
But when you breed one of those white chickens to a chicken of a different color, the white chicken passes on one copy of the recessive white gene. The colored chicken passes on one copy of not-recessive-white. So the chicks show color. What color? Something determined by the genes from the colored parent, and the genes that were hiding (invisible) in the white parent.
That's why some people do not cross colors of chickens. Genes that have no effect when you breed two of the same color (white to white) can become visible when you cross to a different color. So if you want to produce chicks of specific colors, you either breed colors that are known to have compatible genetics, or you study the genetics of the particular chickens you have and learn what they will produce, or you get surprises.
(Crossing chicken colors is not bad, it just provides the opportunity for unexpected results.)