What about the battle of New Orleans? Weren't the British repelled there in that war?
If it wasn't for the American attitudes and tactics during the War of 1812, Canada would have long been a part of the USA. Upper Canada had more than 1/4 and possibly 1/3 of its residents born in the US and they didn't have that much loyalty to the Crown. The French certainly didn't.
Nevertheless, it took this invasion and the burning of the capital (including the Parliament Buildings - which prompted the retaliatory burning of the White House) to unite the United Empire Loyalists and the European born, the French speaking, and the American born. Confederation in 1867 followed.
And Paul Martin is using the same rhetoric today in order to get re elected.