I had this experience 2.5 years ago at Peace Arch border, I was also overstated in USA for 3 weeks. So when I came to US border they told me to go inside the building there was a little line there about 10-15 min, than officer ask for my passport, check some information, than he asked me if I was overstated in USA, so I answer yes, than he type some information on the computer give me some yellow paper to bring it to Canadian border. That itReally? It is a big relief!
I think I read somewhere that US officers take the passport and bring it back. So I thought they do some search or at lease run through their data base or something. Are you sure they are not even typing in the person’s name before they stamp on the passport?
It was for Work permit.
And I came with rental car there