That's commonly assumed, but it's not quite accurate. It's not about "data originating from foreigner". Instead, the criteria[1] is "foreign data" or "data that traveled over a foreign connection". It's not the person that must be foreign, but the data or specific wire on which it travels.

Several sources have explained how the NSA captures domestic data when it travels internationally, such email (gmail) that is stored or processed at a foreign data center. This probably allows almost any data to be captured with some clever packet re-routing.

[1] this may be from one of the infamous "new interpretations" of FISA/etc