If the paths have any legal status can you please show where the legal status can be verified. It is an OSM requirement that anything added to the OSM database must be verifiable to anyone else.

For instance, a PRoW is verifiable via the relevant definitive map. A road name can be verified by a sign.

If the name "Permissive Path" cannot be easily verified then it does not belong in the OSM database.

Regards Bernard.