I'm pretty sure in the UK (where incidentally I can't think of any public land you could hunt on) that there is a concept of an implied easement. That is if you own a patch of land surrounded by another patch of land then you logically must have an easement, or you could never use it.
Scotland has Right to Roam legislation via its Land Reform Act that works pretty well (folks take advantage of it all the time in the highlands), that was an Act of the Scottish Parliament though and only applies to Scotland. The rules in England are not so open IIRC, property law is one of the areas that England and Scotland diverge in approach on a little, its fully devolved to Scotland. The Scottish legislation permits the general public to cross private lands such as farms so long as they respect the property, close all gates etc, don't damage crops and so on.
There have been some instances of abuse of the Scottish system, but its pretty few and far between.
Scotland and England have separate legal systems, hence the confusion - there is no UK wide standard answer on right to roam.
It's actually pretty good law which makes a distinction between innmark and utmark (innmark being cultivated land, grassing fields, gardens and so on and utmark being "wilderness", or everything that is not innmark), gives the public a right to use private roads and man made paths over innmark to reach utmark, protects the "private zone" (houses, including gardens) etc. It balances the publics right to roam with the land owners legitimate interests as good as possible in my opinion.
In England, it's really a wonderful experience. Most fences have points where you can simply walk over the fence and follow a path to some green space. It's ridiculous to think we can create islands of public property only accessible by paying a private land owner (or risking trespass).
Rule is the same in (at least some jurisdictions of) the US. Google easement by necessity if you care to know more.
Trouble in this case is the public owns the BLM land, right? So they would be the ones entitled to an easement and they have not sought one. Perhaps they should.
