Your statement is only true for Harvard, Princeton, Dartmouth and Cornell. For need-aware admission internationally colleges, such as Yale, Columbia, Stanford, UPenn, Caltech, MIT, Duke, Chicago, Johns Hopkins, Northwestern, Washington St Louis, Brown, Williams, Amherst, and Swarthmore, International students do not ask FA as they know that they will be rejected admission if they ask FA and not be the best students in the world.
My congratulations also go to those students accepted by Harvard, Princeton, Dartmouth and Cornell.