It is incorrect. She doesn't have to go to her home country to file divorce since she has lived in usa and new york for a long time as she can divorce in the state of NY as a plantiff.
Information can be found at http://en.wikipedia.org/wiki/New_York_divorce_law
For New York State Supreme Court to have jurisdiction over the parties (see DRL § 230) one of the following residency conditions must be satisfied:
1. The marriage ceremony was performed in New York and either spouse is a resident of the state at the time of the commencement of the action for divorce and resided in the state for a continuous period of one year immediately before the action began.
2. The couple lived as husband and wife in New York and either spouse is a resident of the state at the time of the commencement of the action for divorce and resided in this state for a continuous period of one year immediately before the action began.
3. The grounds for divorce occurred in New York and either spouse is a resident of the state at the time of the commencement of the action for divorce and resided in the state for a continuous period of one year immediately before the action began.
4. The grounds for divorce occurred in New York and both spouses are New York residents at the time the action is commenced.
5. If the parties were married outside of New York and have never lived together as husband and wife in the state and the grounds for divorce did not occur in New York then, one spouse must presently be a resident of New York and have resided continuously in the state for at least two years prior to filing an action for divorce.