Indeed - which also resolves this issue:
Barnard would be her “no core” option at Columbia University. 
Since they are full-pay, I’m not sure that this is necessarily true.
I don’t know how common that his, but in case of Barnard:
We broadly define international students to be 1) a citizen of a country other than the United States who has been educated abroad; 2) a U.S. citizen educated abroad; or 3) a Foreign National educated in the U.S.
However, as far as need as a decision factor:
We are need-blind for first-year US citizens and permanent residents