Your facts book was mistaken if it claimed the flag in question was American. I did give you the "reason" the flag on the bill is what it is. It is not the American flag after all; it is the flag of Ontario, where the building is located. My source for the answer is a Canadian citizen on a message board who was answering the same question.
You haven't wasted any money if you choose to not accept my answer. I personally believe I am entitled to credit for doing the research and debunking the assumption in your question, but that is your decision.
By the way, if you HAVE a Canadian $2 bill, I advise you hold onto it, especially if it is in good condition. Also Canadian $1 bills.
They are not made anymore. The $1 has been pulled from circulation some years ago and I am sure the $2 bill will be also, if not already.