You are absolutely right. However, consider now that USA invades Canada as a result of this. This is infinity worse and always unacceptable. Nobody—not even American citizens—would tolerate that.
The last time USA invaded a foreign country under a false pretense we saw the biggest protests in US history. But then I do have to admit that Bush was reelected in the next election, so perhaps you are right and I am wrong.
Given what we have seen American citizens tolerate in the past, I expect public opinion not only to support such an invasion, but for Americans to enthusiastically participate.
In fact, some redneck militia trying to invade Canada is a common trope in US entertainment (from South Park over to The West Wing, even a whole movie exists), implying that it would be pretty easy. It's played for laughs, but it adds to the desensitisation of the public opinion about such an endeavour. Consent is manufactured.
