There is no rule, anywhere, that says that an American citizen living outside the United State (or, for that matter, in the District of Columbia, or Guam, or Guantanamo) must be treated as a resident by some state for public university tuition purposes. Personally, I find the whole idea of in-state / out-of-state tuition differences offensive and counterproductive, but they are well established. Few, if any, kids whose families have spent their pre-college years outside the U.S. will qualify under any public university residency definition.
So, as others have suggested, it makes sense to look for universities without much of a distinction in tuition and fees, for universities that award a fairly high number of merit scholarships to OOS students to bring them even with resident students, or for the small minority of public universities that allow a student to establish residency while attending the university.
Actually, any student who graduates from a public or private high school in New York State – even if the student lives out of state – is entitled to in-state tuition at SUNY (not sure about CUNY). There was a famous lawsuit about this, in which Binghamton was charging OOS tuition to a bunch of students from NJ who graduated HS in NY (for those of you not from the area, it is close enough that there are students who commute to private schools in NY from NJ or Connecticut). After the students graduated, they learned that they should have been charged in-state tuition and sued for the difference. Binghamton said it was the students’ responsibility to ask for it at the time; the students said that it was Binghamton’s responsibility to charge them the correct tuition. The students won.