When anyone has the power to edit supposed facts on a website like Wikipedia, that justifies suspicion.Most of what is on Wikipedia is accurate. But you don't have to believe that website. If your chickens don't breed true, then you do not have a breed of chicken.
What you are describing would be a hybrid. That would not be a breed of chicken.
You can create the California White, which is a hybrid, by crossing a California Gray rooster with a White Leghorn hen. The California White is not a breed.
By the way, it is California Gray. Gray with an a. I know the color can be spelled Gray or Grey. But the breed name is California Gray.
Many breeds are the result of hybridization.
Right on the California White.
I've never seen grey spelled like "gray" except in a last name. Habit I guess. They are CA Grays. Privett and Stromberg were the only ones who had them. I guess you could ask one of their breeders whether or not they are true CA Grays.