And there are probably other confounding factors; eg, it may be much more difficult for a homeless individual to exist in a rural town than a city - the stats would show that as more homeless in the city, even though the ambient conditions are better. So sure the stats say that there is more poverty in the cities - but that might just be signalling that poverty is much more painful in rural areas. This means that people could be saying things that are technically wrong (hence the myth) but are very accurate to the lived experiences and pressures on someone in a rural area.
Only a small number of people need things that a rural hospital can not offer. Meanwhile, everyone needs things (food, housing, etc.) that are much more expensive in the city. Likewise, cheap housing can mean that it’s much easier to afford to live in a decent school district. And the same amount of government funding for say schools goes further in rural areas. In NAEP tests, rural schools perform comparably to suburban schools, and better than urban schools: https://nces.ed.gov/programs/coe/figures/images/figure-tla-5...