There are several problems with the land status shown on GPS chips and maps also for that matter. First, they only represent what the status was at the time of the data being printed or made available to the public. Generally private property records are kept with individual counties. The counties don't update their maps with every status change. Our county is sometimes months behind. A perfect example is my own street address. The county changed the name of the county road I live on, so immediately the gps in my truck & car is wrong, as is my handheld. I put in my old address and of course the road sign doesn't match, put in the new address and it comes up "No Such Address". The whole point is that the gps data is only as good as what it receives. Remember that old saying "Garbage in...garbage out"! Forest Service & BLM maps are almost never current either. Just look at the published date.
As far as fences go, you just never know. Here in our NF, all of the grazing leases are fenced. Doesn't mean you can't enter the land. But they are never signed either, so it is impossible to really tell if it is a private inholding or a grazing lease. I also think that the rules vary a lot. Here in Colorado the cow operation leases the land for grazing only during a specific time period, usually June thru mid October. Blm is pretty much the same. I know lots of leases in Wyoming are year round. Here they are not treated like private property, the public has access. Totally different in Wyoming. My suggestion is to check with the agency in the area you are wanting to hunt for the latest information.
Complicated...you bet!