Sanity check: the sinc function only introduces ringing when there are frequency components of the unfiltered function greater than the imposed bandwidth, right?
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Yes, that's correct.
I was curious how the problems shown in the graph here were defined. It was interesting to find out that this graph was the result of experiments with human subjects! As Mitchell and Netravali put it in their paper: "The response of human viewers to various spatial effects of filters is not yet a well-understood science and is largely subjective in nature."
So, here are we choosing r_min to be min(cell_width, cell_height)?
I could see this effect as actually being desirable in some cases, either from an artistic perspective, or when you need to enhance edge contrast to make an image easier to make out. Definitely doesn't look realistic, though.