Real-life experiences would seem to indicate this is not the case.
See worked examples in Venezuela, Argentina, Ecuador, Serbia and Syria. Small rural enclaves get overrun and pillaged by Government-sponsored militia from the cities. Whoever controls the cities usually dominates the surrounding areas.
That bug-out location in the middle of nowhere gets wiped out by local bandits - or becomes the headquarters for the local bandits.
Small towns and major suburbs around the cities may do very well. Central urban cores often get wrecked during factional disputes and they will not repaired for the next twenty years or so. Unpopular minorities who used to live in those areas are expelled.
"The Troubles" are highly localized. One hundred miles away, life may appear to go on as though nothing is happening. It is very deceptive. The troubles appear in waves which pass from one metro area to another.
Small groups with good organization and access to support from outside the immediate area will usually prevail.
You are forgetting one thing. In those foreign examples, the countryside isn’t armed to the teeth. They are mostly very simple farmers. In middle America, vets are everywhere, guns are common.
In US cities, both are very rare.
There will be no government militias coming out of the cities. No other nation on earth has the US tradition of hunting and marksmanship with rifles far better than most nations scarce sniper rifles.
American city people will not be able to dominate our rural people.