I've added the owner key/tag and set it to private. I wasn't sure how to do it on this changeset. 

I believe there are signs. I see in the wiki that OSM doesn't give much credibility to government datasets, but as a government employee of this county I can assure you that this road is in fact not publicly owned. If you need evidence please see public roads here: 
https://www.arcgis.com/apps/webappviewer/index.html?id=9e4ce6f2a346453c8ec71c4eff6b9d5a
And land ownership here: https://cp.spokanecounty.org/scout/map/?PID=27276.9060