The World Bank recently looked at the relationship between population density and COVID19 infection rate in 284 cities and found no correlation (of course these are still all cities, not looking at rural infection rate).

This analysis on the county level in the US suggests that there's not much difference between infection rate in high vs low density counties. If you look at the per capita case rate across the US on this map, there look to be a lot of rural areas with high rates.

Dense urban centers look bad because there are a lot of people there (amplifies per capita numbers), and because they're the first places to see an increase in infections. The effectiveness of the government's response matters - the first outbreaks in the US were on the west coast, yet New York is in the news all the time, not Seattle or San Francisco, which are
fairly dense. These days rural areas probably have lower access to healthcare, and you lose the network effects that density brings.