Don’t think rural areas in the USA are going to fare much better. Most of our food comes from mega farms in the mid-west, the California central valley, and places like that. Most rural areas, at least east of the Mississippi river, though more spread out than urban areas, are still quite populated.
I live in a small town in rural Northeastern Vermont. If we were cut off from re-supply by a major SHTF situation, the food would hold out longer than an urban area, but not that much longer. The small farms dotting the landscape would quickly run dry. Most people in rural areas do the same kinds of jobs as urban populations, still get most of their food and dry goods shipped in from far away, and shop at Amazon.com and Walmart.
Hunting and fishing would quickly deplete the available game. After that, what you would have is a lot of hungry people, a large percentage of which have a hunting rifle and a few boxes of ammo. And as Selco points out in his “Blending in and Survivalist Hate” post, they will not be very friendly.