University research has been corporate-funded for decades.
I don't know what other fields are like, but for biomedical research this is absolutely wrong. I worked for both public and private universities in the US for 15 years and the vast majority of scientists were getting the vast majority of their funding from the NIH, or maybe the NSF, plus a few big private foundations like HHMI. Funding from companies was not uncommon - in fact it paid my salary for a couple of years, thank you tech transfer department* - but for most researchers it was a fraction of whatever the government was giving them. (In the group where I was paid by corporate money, I was the only one, while another dozen people were paid by an NIH grant.)
(* actually, no. Working with companies as an academic can be an incredible pain in the ass and I didn't like our licensing policies anyway. And it certainly did skew our priorities somewhat, which was even more annoying. But we absolutely didn't need the money either.)