@mpjgregoire @bgcarlisle My Oxford Canadian Dictionary disagrees with CBC! The entry for "tuque" says it's a variant of "toque."
The entry for "toque" does mention the chef's hat, but that's the third definition. The first is the typically Canadian knitted winter cap (with or without a tassle or pompom).
HOWEVER...Canadian Press style, which CBC would follow, says it's "tuque" for a knitted cap, and "toque" in all other cases.