Probably or DOD. May just be administered by the FS though. I bet that road is not gated if that's what you're concerned about. You can always call the Los Padres NF, Monterey District office and ask.
Los Padres National Forest - Alerts & Notices
CalTopo is a very useful mapping site. You can overlay different maps like topo maps, FS maps, Google, etc. Play around with it. The link below has a USGS topo map overlayed with the Forest Service map along with color coded land management boundaries.
CalTopo - Backcountry Mapping Evolved
Good luck!