Princeton list price is about $91k (first two years) or $93k (last two years) with tuition being $65k of that.
So if your example with $200k parent income gives a net price of $13k, then Princeton is offering $78-80k of grants, which is more than the $65k tuition.
Probably it meant that Princeton was already that generous, and decided to make an announcement on that, without becoming even more generous. Of course, getting admitted is the hard part, and it is much easier to gain the necessarily admission credentials to get admitted to Princeton from a high resource environment (about 40% of Princeton undergraduates do not get any financial aid grants, and some of those who do are getting lower amounts; Pell grant students are, as expected, under-represented at 19%).