The implication of the title, that rural cities in general have overtaken NYC isn't necessarily backed up by the data, unless it can be shown to be a pattern in a huge number of rural cities, such the the combined population of those reaches a level of statistical significance. The data in the NYT article also shows more rural cities that have lower case rates than NYC. The more likely scenario is that these rural ci…
The observation actually perfectly fits a statistical principle that you're just going to see more extremes (lower and larger per capital cases) in smaller populations because probability.
I don't think we have enough data in those places to know the patterns either way, especially since the situation is changed daily. The dynamics of this disease aren't well understood enough. Earlier it was thought that the heat of the southern hemisphere was protecting it, but now Latin America is seeing a large rise in cases.
EDIT: removed my comment about low sample size and high variance, since the case rate is just a about cases/100 people, not based on a sampling procedure.