I think, actually, this statement is misguided, for a couple reasons. Its very likely that people are underestimating the average city's "hospital beds per capita" metric; frankly, a ton of people live in the average city (duh). Are there enough beds in many of America's tier-2 (say, Austin) and tier-3 (say, Cleveland) cities to cover all of the population?

By comparison, outside of cities, the spread will be far, far slower than within. Yes, healthcare is worse, but there's an order of magnitude fewer cases. People travel less. They go to the store once every two weeks, not every 4 days, even when there isn't a quarantine. They don't visit the new hipster restaurant down the street. They don't live twenty feet away from their neighbors.

NYC has 25% of all of the United State's cases, despite having ~2% of the US's population. This is the same story that is playing out in every state. Let's take Indiana as an example, being that they're having a relatively moderate outbreak with mostly rural areas surrounding a top 15 US city by population: Indianapolis has 41% of the state's cases, despite representing ~12% of the state's population.

This shouldn't be a surprise; diseases spread faster in cities. But, what you're asserting is that, eventually, rural areas will see the same spread that cities are. This feels misguided. That isn't to say that some, or even most, rural hospitals wont be "running hot" for a really long time, and that the virus wont spread and these areas, but its simply unlikely that the situation will ever be as bad as in major cities.