It's incredible seeing this on hn. For context, while the FoHo is sometimes good for very, very breaking and recent stories, it's a little hard to overdo the niche it fits in Stanford culture: it's pretty much the main and only tabloid for fast-paced news and (sometimes) absurd 'takes' on things happening around campus.
While I don't doubt the story, I would always take it with a grain of salt. I don't personally know the person they claim is running these "under the table" tests, but the tests are very simple, so it wouldn't surprise me if it was actually true. (Most first or second year biology/bioengineering students can easily run RT-PCR without an issue, especially if they already have the primers available.)
EDIT: I was just contacted by one of my friends who knows of a few students and their labs doing this. Apparently there is more than one.