Would "200 students are better than none" be invalid? When you swap out the number with some other word i.e. "Some students is better than none", using "are" is the correct choice.
"200 students are better than me" means that there are 200 all of which are better than me, it's not grouping them together, just counting them. "200 students is better than me" would mean that as a collective they are better than me, but I might well be better than each of them individually.
Someone should design a small set, each in monochrome, to fit on A4 / Letter size paper, with simple explanation and example sentences.