So we could look at Marshall Scholarship winners:
http://publicuniversityhonors.com/2014/12/06/marshall-scholars-2015-eleven-public-university-winners/
In 2015, out of 31, there were 11 from publics (6 from honors programs). 4 from LACs (not all of them elite). (Also 2 from Catholics, 10 from Ivy/equivalent RU’s; the rest from Olin, Naval Academy, and NEU; and that’s only 30 but I’m not going to hunt down where the miscounting is).
In 2014, out of 34, 11 were from publics (8 from honors programs) vs.
1 from a LAC (not elite). Also 2 from Catholics, 17 from Ivy/equivalent RU’s.
http://publicuniversityhonors.com/2013/12/10/marshall-scholars-2014-public-university-honors-students-win-8-awards/