You're completely correct. I've updated the access tags. Sorry for the poor original modification!

I believe your edit has removed a route designated as a public bridleway (i.e. with legal status). As the route went through a river (via a ford) and across a heavily overgrown field I can understand why it isn't used for routing. However, the routing software should make use of the data available and the data should have been changed to provide more suitable information (e.g. adding depth of ford). Removing a legal route from OSM isn't the way to influence the routing soffware