Someone told me one time, any airport where you can get a direct connection to another airport that has airlines that fly out of the US, you can use the International Airport designation. The trouble with that, just about any airport would become eligible for the international designation. I have come across some truly small international airport, but I'm still not sure how the designation is assigned. While these example aren't really small airports, I don't think Bellingham, in Bellingham, WA nor Hancock in Syracuse, NY fly internationally, with the possible exception of Canada.
How the heck does this work???