Today this policy applies to (non-Jewish) white people. We call it affirmative action.
According to Harvard's website, 44% of students in the Class of 2016 are "minorities." Jewish percentage not listed, of course, but other sources say "over 30%," whatever that means. Rather wildly over-represented given their 1.7% of US population. Though both of these numbers depend on how you define the group in question.
This leaves <26% available for non-Jewish white people, even though they make up 72% of the population. (Less than that in the relevant age group, of course.)
As a member of the Board of Overseers (not directors), Roosevelt presumably did he did have a hand in approving the policy -- to his discredit -- but it wasn't an idea he came up with. It came from the administration of President Lowell.
Roosevelt's own boastfulness may have given Medoff the impression that it was FDR's own idea, but it's sloppy on Medoff's part not to examine further. FWIW, FDR did oppose Lowell's plan to create a segregated "Jim Crow" dorm for African-American students (this at at a time when some colleges like Princeton weren't even admitting Black students).