Approx 7 years ago my step daughter (a Canadian ) was attending college in Ontario, Canada.
She got pulled over by Canada Customs
She was driving a US (Michigan) plated vehicle
She had a resident alien (green) card
She had a Michigan Driver's licence.
IOW she was a legal US resident.
The Border agent was about to impound the vehicle until duty and taxes were paid. My daughter tried to phone me to be told "Turn that phone off - NOW!"
A Supervisor got involved and, after 5 hours(!) decided, as it was her last trip o the term, they would let her in "this time".
I got hold of a Superintendent responsible for this stuff who was incredulous that this had happened. She kept repeating "But she lives in Michigan, it doesn't matter if she is a Canadian".
I got a profuse apology and a promise.....
"Perhaps the border agent did not know any differently, but the Supervisor certainly should have. I will talk to them."
We ended up with a letter from this person authorizing my daughter to cross with her car while attending college.
Wouldn't you know, she got challenged at the start of the next term, so she produced the letter, to be accused of forging it!
Fortunately she had the presence of mind to say "There's the phone number of the person who wrote it, why don't you call them?"
End of discussion.
Bottom line - even if you are in the right they can give you grief.
If you are a Canadian with a primary residence in Canada, I strongly suggest you DO NOT try to drive across the border with a US plated vehicle unless you have an American friend doing the driving at that point.
When I lived in Ontario I had a run-in with them over a rental car one time too, but that's another story