The second example adds statistical noise, but does not invalidate Graham's procedure. In the absence of noise, the distribution of accepted people will be H(x-C) f(x) for the main group, and H(x-C-K)g(x) for the other group (where H(x) is a step function, f(x) and g(x) are the distributions of quality of the two groups).

If noise is present, then you get convolve(H(x-C)f(x), k(x)) instead, where k(x) is the pdf of the noise distribution.

You'll need more samples to measure this, but it's completely measurable via Graham's method.