You can achieve the desired behavier by associating the permission with the corresponding feature:
This does work though the code looks a bit repetitive and I do see here an opportunity for improving the API. The next release will associate the permission either with its own Feature of with the Feature of the parent folder (depending on which one is initialized). And the DirPermission.Feature will be marked as obsolete to prepare it for an imminent phasing out.
new Dir(docs, "logdocs", new DirPermission("Everyone", GenericPermission.All) { Feature = docs }