This is true for public universities and private universities; you see the same thing happening in academic papers (and especially the university PR around the paper)
The actual papers don't overhype. But the university PR's regarding those papers? They can really overhype the results. And of course, the media then takes it up an extra order of magnitude.
I've definitely seen many examples of papers where the conclusions went far beyond what the actual results warranted. Scientists are incentivized to claim their discovery generalizes as much as possible.
But yes, it's normally: "science paper says an experiment in mice shows promising results in cancer treatment" then "University PR says a new treatment for cancer is around the corner" and "Media says cure for all cancer"
> As a field, I believe that we tend to suffer from what might be called serial silver bulletism, defined as follows: the tendency to believe in a silver bullet for AI, coupled with the belief that previous beliefs about silver bullets were hopelessly naive.
(H. J. Levesque. On our best behaviour. Artificial Intelligence, 212:27–35, 2014.)