You know, I'm on similar situation. The difference is, I have already been accepted to the grad school outside the USA, but they have not sent me any details of financial assistance or formal offer letter at this point.
admissionprof should be the best to answer this one....
The resolution signed by virtually all US schools says that any acceptance still in effect after April 15th is binding, and can't be rescinded without written permission of the university involved. This is firm.
That said, what can they do about it? It has happened to us once, when a student got a better offer in mid-May and asked us to give written permission to allow them to accept it. Of course, we gave the permission--we don't want to force someone to go here. We were mightily pissed though, since we had a full class and had turned someone down because this spot was full. I also remember the student's name, and if they apply here for a faculty job or postdoc, will not forget (but no, I won't launch a vendetta against them by telling other institutions). So you will almost certainly make some professors angry at you.
I understand the dilemma though. How about the following thought: complete honesty. Tell the school you've been accepted at exactly the situation, including the name of the non-US school, and that you are accepting their offer. They may have a suggestion. If that happened to me, I'd probably call the admissions person at the non-US school, and get an unofficial off-the-record estimate, not to be shared with anyone, about the odds that funding will materialize. Then I'd base decisions about our waitlist on those odds. And I wouldn't be upset at the student if they ended up going to the non-US school.