Re: Green card...
As a Canadian, when I researched this issue I was informed (can't find the documentation just now) that even running an online business that is based in Canada but which I may access from the US is considered "working in the US".
I think I would adopt a "don't ask, don't tell" policy. You may need to be careful which IP addresses you access if push came to shove though.
Why are people happy to accept science which makes their life easier while rejecting science that makes their faith or beliefs more difficult?