re:
" …I don’t really know much about how the land grant colleges at Cornell work,…"
Hope this helps:
https://en.wikipedia.org/wiki/Statutory_college
Always politics involved:
http://www.nytimes.com/1996/02/21/nyregion/can-suny-afford-cornell-officials-are-questioning-division-of-state-support.html
No idea about the “free tuition” thing though, sorry…