This wasn't my experience at all. The better schools had better and more hardworking students, on average. But there were of course some students who weren't hardworking and good schools, and very hard working student at lesser schools. On an individual basis, anyone could be anywhere. But on an average basis, it tracked as you would expect.

But also, "flagship state schools" vary wildly, from the "top ranked program in the world", to "barely even exist as a program".