I don't know, but see no reason why that should be the case. There's a sidewalk, you just didn't want to use it. Walking on someone's property just because it fronts a road wouldn't seem to be appropriate. The County has no easement, neither do you, and it's not public land. In practical terms it's doubtful the homeowner has any real recourse against you, but I suspect you were in fact trespassing.
The County does require sidewalks in subdivisions, but not necessarily on both sides of a street, depending on lot sizes. The sidewalk has to be within the dedicated right of way of the street.
https://online.encodeplus.com/regs/fairfaxcounty-va-pfm/doc-viewer.aspx?secid=423#secid-423