I've done quite a bit of exploring on remote mine claims. One of the problems I've encountered is that many claims are BLM or USFS land and totally open to the public. The only thing not open to the public is mining on a particular claim. However, a lot of these claims are occupied by some very strange, very anti-government, very well armed folks. They pay about $100/year to live there and have to prove to the gov'ment that they are actually mining something. I'm not talking patended claims that are private land, just regular 'ol mine claims on public land.
I never trespass against a sign, even when I'm sure I'm still on public land, but that doesn't stop people from being extremely defensive about their mine claims, especially if they occupy them year round.
The first question I always get asked is if I'm BLM. When I say no, they start with the attitude. I have every right to pass through and be there, but they often don't see it that way. They think they own the land and can regulate access, even though they can't. And because they are usually anti-government, they have little or no respect for government laws.
The best defenese is just to avoid the occupied claims altogether. After that, making it very clear that you're not trying jump their claim and some sweet talking and pretending that you have the same anti-government feelings about them "damn BLM" people goes a long way to making friends. As much as I'd love to tell some of these folks where they can shove it, I've found that being appologetic and friendly is the best way to avoid what could end up being a violent confrontation in the middle of nowhere. In the end, I've shaken the hand of everyone I've met so far and left peacefully.
Of course, not all folks that live on mine claims are like this and living in a remote area, under constant threat of eviction does tend to make people a little off center, but
I've run into a more than my share of these guys. It goes with the territory of what I do in my spare time.