Self-promotion tends to help specific universities and researchers. If my name make NY Times, that's a big deal. On the other hand, blame is diffuse. People start to distrust the scientific establishment as a whole.
Successful scientists themselves tend to grandstand and overstate their work when talking to the popular media. Idealistic grad students don't do that, but idealistic grad students also don't get faculty jobs and later tenure (politically savvy graduate students do).
Unfortunately, dishonest, shameless self-promotion is how one gets ahead in the academy, and how universities get ahead of each other, even if it is a lot like pissing in a big, common, shared pool. You get a slap-on-the-wrist for bad research results in a scientific journal. That doesn't happen for the popular press.
It depends on the school too. I'd love to see a replicability study based on school tier. I bet hyper-competitive schools (Stanford, MIT, Harvard, and the rest of the Ivy+) would come in far behind state schools for replicable results.