These students did absolutely nothing wrong.

They submitted their paper to a well known, well regarded preprint service (arXiv), which is pretty normal for a number of fields.

Then, presumably, the paper would go to peer review. Where one would hope the reviewers would point out a few glaring flaws (like that an SIR model without either the creation of new susceptibles or waning immunity must go to 0 and they are 'dooming themselves to success').

The paper would get rejected, or heavily revised, and the world would keep spinning.

They didn't actually do anything wrong. If you want to blame someone, blame an overexcited media that grabbed something off a preprint server and ran with it, knowing full well arXiv has no 'Is this right' quality checks, and isn't peer reviewed.