I grew up in a rural area as well but in my mind it is no different or possibly worse - farther distances meant biking was a necessity versus walking, zero bike infrastructure so I had to be commingled with vehicular traffic, and that traffic was going much faster than in a city due to the wide openness of the roads and no need to stop for far distances. I think it was far more dangerous.
I think you need to give the country, as the infrastructure in a rural area varies widely.
In Britain every road is for cars, and in rural areas they can travel at 80km/h on them. There will be footpaths within a village, but not necessarily on the roads between villages. Cycling on footpaths is illegal, including for teenagers.
Other countries (Netherlands, Denmark, probably more) can have roads only for use by residents or farmers plus cyclists/pedestrians (e.g. gates at each end), or roads with much lower speed limits, or guaranteed footpaths. I've visited but not lived in a rural area like this, so I'm not sure how well it works in practise.
Survivorship bias. The rural kids riding their bikes all over the place who unfortunately got eliminated by cars didn't get to write hacker news posts.
My own 6 year old has to cross a busy main road to get to school. Have I damaged him mentally by personally making sure he gets across twice a day, or have I mitigated the low risk of a catastrophic outcome?
Rural places can be, and should be, one of the best places for independent mobility in kids, but unfortunately are often the worst, since you have no footpaths (aka sidewalk or pavement) and the roads are full of high speed traffic with no shoulder.
