(1) "Ivy League" means absolutely nothing in the context of graduate programs, as the rankings are discipline-specific and many Ivy League grad programs are mediocre. For example, Harvard's computer science program is strong, but not remotely in the same league as CMU or UIUC.
(2) In any case, "Ivy League" is not a synonym for "elite college"; well-regarded universities such as Stanford, MIT, and Michigan are (surprisingly?) not Ivy League.
(3) Related to (2), emphasizing "Ivy League" pisses off nearly everyone who went to a good college. Those who went to non-Ivy elites (like me) consider themselves excluded when they see these ads. Those who went to Ivy League colleges generally dislike the snooty, stuffy connotations of "Ivy League" and don't like the sorts of people who emphasize "Ivy".