Routinely happens to us. We made an offer (full time) to a graduating PhD student (US university) from one of the famous deep learning professors (one of three who won a Turing award recently). The guy really like our team and project yet he had Chinese citizenship and when declining our offer said he simply chose Canada vs US.
As an international student who went to a top US university, I'm faced with a similar situation when it comes to H1B. I understand I have no inherent right to be here, and that part of the reason why H1Bs are difficult to get is because of the many frivoulous petitions on behalf of my countrymen from large IT consultancy companies from my company. But when it comes the option between US and Canada, I'd rather pick Canada just for the peace of mind, even though I'd prefer to work in the US and the salaries in Canada are much lower.
