Hi there. Whether or not a road is on private property on a "GIS map" is immaterial to how it should be tagged in OSM. It is possible for a public road to be on private property, such as via an easement, or when the GIS is out of date. Further, any GIS data you are using to cross reference against OSM needs to be vetted through the import process. See https://wiki.openstreetmap.org/wiki/How_We_Map "don't copy copyrighted data without permission"

We need a written sign off from the city that they are ok with you using their data to update OSM unless the city's data is public domain.

Before referencing any more city maps into OSM, I suggest proposing an import following the instructions here: https://wiki.openstreetmap.org/wiki/Import

Thanks,  

Elliott Plack  
OSMF Data Working Group