You just have to look at the ethnic mix in the school system, both public and private, in affluent areas of Vancouver (and Richmond) to see that the children are not "overwhelmingly white".   In fact the Caucasian demographic is a minority.

In the most most affluent areas of Richmond like Terra Nova and Westwind, home to expensive homes and no social housing, the Caucasian school demographic would be at about 20%.   

In my west Richmond neighbourhood, the school playgrounds have very few Caucasian children.