Just to interrogate this description:

So, there is a trick to picking the points such that any can be lost, and only the remaining number matters? I think this was the case with par2, that used RS - you could lose any of the files, and as long as you had enough left, you could infer the lost files. I guess this method is the bit I get stuck on.

How are 'corrupt' points detected? By determining that no polynomial is described by a set of points, and then computing the least number of points needed to remove for a polynomial-describing set of points?