The first Stay At Home order for NC closed many types of businesses but didn't have any mention of staying within a short distance of someone's home. The
FAQ from late March specifically encouraged outdoor exercise. The rules were adjusted a bit in April and May for outdoor activities, but there was never a time or distance limitation for being away from home. The focus was on the 3Ws: Wear, Wait (6-ft distancing), Wash (hands).
Coming up with restrictions that make enough sense for most people to follow them is a balancing act. Only issuing recommendations clearly doesn't seem to be enough. But if restrictions seem to go overboard to most people, that can be a problem too.
The problem for most European countries seems to be that they didn't stick with mask mandates after the worst was over in the spring. Not sure why the slow but steady increases in Aug-Sep weren't enough for changes to be made in the approach taking by most European governments. Very different situation than developed countries in Asia, Australia, and New Zealand.
From NC Stay At Home Order FAQ:
Can I leave my home to exercise?
People are encouraged to maintain healthy lifestyles, including outdoor recreational activity, such as walking pets and jogging. While exercising, individuals should maintain social distancing and continue to take protective measures to maintain their personal health and wellbeing.
Does this Order prohibit outside group exercise?
As long as the group abides by the mass gatherings provision in the Order (no more than 10 people) and maintains adequate social distancing, this activity is not prohibited, but it is strongly discouraged.
Can I take my kids to the park?
Unless your local jurisdiction has closed parks, people may go to public parks and open outdoor recreation areas while following social distancing and mass gathering guidelines. Public playgrounds and their equipment are closed for use statewide.