Medical research is a profit center for many universities, not a cost center. They get funded by grants from external entities like the NIH and get to skim off the top of each grant for overhead. As one outsized example, my alma mater got $583MM in NIH grants in one year. I'm not saying universities don't fund research from their own coffers, but it's important to understand how much funding comes from the government and from other sources.
I wasn't addressing that. I was solely addressing the idea that universities were teaching centers that do research ancillary. A lot of them would consider that backwards. They're research institutions that also teach.