Well I believe that the majority of this land south of the San Francisco is BLM land. The road that I went in on was the Black Hills Back Country Byway as found in the link below. I think that the fence line is to separate the various grazing areas. Near the southern Gila crossing you would run into private holdings if you ventured east of the bridge or across the bridge. I'd like to get to the old station site at Guthrie but I don't know if that is possible with the private holdings down there.
BTW, here is an overlay of the station site at Guthrie. The old oil storage tank outlines can still be seen in the aerial photo.
Guthrie Overlay
BLM Black Hils
Dave