I don't think that's correct. British Regulars redeployed from the Napoleonic Wars burned down the White House. But if you're referring to the fact that it it was largely in retaliation for the sack of York (now Tornoto) by the Americans, then you'd be correct.

That's not to diminish Canadian achievements in the war; they seriously mauled American attempts at invasion and held Detroit at once point. Canada was very much a British colony at this time, and was just beginning to form a sense of national identity (of which the was would play a large part.)

Glad all that mess is behind us. =)