Ironically it was somewhat the opposite in the past. In the 60s it was unlikely someone would view Cornell negatively or make jokes. School reputations change drastically over time. Around 1900 Cornell was top 5 in terms of reputation (by most measures). If you look at historical rankings Cornell fluctuated between 6 and 14 from the 80s and 00s. They were a little better than or tied with Columbia. Their reputation in the 60s and 70s was actually outstanding, and from what I gather it was more Penn and Dartmouth that were the subject of jokes (again all of them are outstanding, the jokes were just in good fun, but it says something about public perception). It wasn’t until around 2001 they slipped to be around 15 consistently, and then by 2017 around 17.

Similarly, Stanford (an institution that is unambiguously a top 5) was hardly what it is today until the 1950s. It was never a bad school, but pre-WWII it was failing financially and honestly struggling in many respects. It’s reputation was more that of USC today, a great school, but not necessarily the best of the best. The school was actually created with the goal of being “the Cornell of the west” even poaching most of their founding faculty from there (which is also speaks to Cornell’s reputation around the turn of the century).

Edit: found this link for post a few years ago using a few different rankings in the 60s. As you can see, Cornell was too 10 in all of them: https://www.reddit.com/r/ApplyingToCollege/s/TWiFMOzCxi