Yeah that's fine, josm filled in the non-plural version in error

I've been "made aware" of this commit and got to say I agree with DaveF - the access tags refer to the paths themselves and not the land they go over.

Looking at the Wiki it seems that *=designated is to limit a path to only these forms of transport, where as "access" is for whom is allowed to use a way, i.e. the access would override them (e.g. close during long-term construction works, or only usable by people heading to a destination).

highway=footway would be sufficient to limit use to only foot traffic.

AFAICT we should be tagging the landuse (or similar) with the access=private, but not doing so on the footpaths.