I wasn't too worried about this talk of residency and ownership requirements until just recently. But, the form posted by WebSiteBilling indicates that information about the merchant's "Principles" is required by Visa; things like address, SSN and so on.
http://www.websitebilling.com/visaregform.doc
Will Visa cut you off if the company's "Principle" is not American? No one can say. This uncertainty is very scary. For the last week I've been thinking the "safe play" is set up a Nevada LLC and do whatever else Visa requires, so I can easily keep my rebills and affiliates. Now I'm not so sure if that is the safe play for international websites. Being cut off without notice by Visa is nearly a worst-case scenario.