I worked at SU (in a department closely aligned with ESF) for awhile so I know a bit about this. Cornell is a little different because those students are actually Cornell students (they just pay less) meaning their diploma says "Cornell". While ESF is actually very good, it does not have the name recognition (nationally at least) of Syracuse or Cornell.Similar situation hold true for SUNY ESF (env. science and forestry) at SU and some of land-grant majors at Cornell. Students in those programs are taking courses along side other Cornell and SU students and are paying a fifth of the tuition.
Additionally, It is not at all unusual for closely affiliated universities to allow students to take a limited number of courses at the affiliated schools. For example, NCSU/UNC/Duke allow students to take classes at each institution regardless of their home institution. While at UNC, I took classes at both NCSU and Duke. Interesting, more Duke students take classes at UNC than the reverse (or that used to be the case...I can't find the current numbers).