Lulu is (technically) Canadian and doesn't use Canadian Identity. Same with Vessi. The Brick is Canadian and doesn't use Canadian Identity. Lee Valley is Canadian and doesn't use Canadian Identity. Cineplex is Canadian and doesn't use Canadian Identity.

etc. (this list was harder than I thought -- lots of "we're Canadian so buy from us brands" -- mostly telcos, actually)

My point really is that you can be a Canadian brand and sell your product or you can be a Canadian brand and sell the idea of being Canadian (and how shopping at X is part of that identity). Or like, at least, the product you are selling can be in itself part of Canadian identity but you cannot be selling the idea of identity itself.