Covid takes a few days to show up on tests but it also takes a few days to become contagious. Symptoms onset is usually after ~4 days and you're contagious for ~48 hours before that. If you're tested during the 2-4 day pre-symptomatic period, you'll show up positive. This does mean you could be contagious for ~1 day before your next test, but we're honestly splitting hairs here. You'll also show up positive if you're asymptomatic and contagious.

Also the idea that OP's post is dangerous misinformation is pretty ridiculous in my opinion. We had to institute strict social distancing early on in the pandemic because we had no diagnostic test and the virus was already widespread. Neither of those things are still true in Boston which means that the situation is materially different once people get through the initial testing/quarantine. If we can prove that someone didn't bring the virus with them, then the risk that they will spread the virus to others drops significantly, especially if they primarily interact with other people that have tested negative. We can say this with a good amount of confidence.

I also addressed your concern in my previous comment. Testing really should be done every other day and Northeastern easily could have achieved this by making more students take only online classes (or by incentivizing gap semesters). But they would never do that because of the financial implications. I also don't expect them to lift the guidelines in any noticeable way. They need to get through January 15th to get a full year of in-person tuition and that's all they actually care about.