DCR -- Yes. The very reason no one calls you is that you're not there. You're 1.5 hours away. That would be silly.
And you're right. Mike has no legal responsibility nor obligation to any authority (but his Maker) to help anyone. But the fact is, that Mike DOES live where he does, and people DO drive and get stuck on BLM routes, and people DO call him, including the Sheriff, FS, and the BLM.
BTW, there's talk of Mike being monitarily compensated for performing these rescues that would otherwise be handled by public agencies. How does that rub ya?
Also, you do realize that the public CAN be thrown off public lands by public officials, dont' you? There's no guarantee that even if you did show up at public lands that you'd be able to get in or stay in. In fact, I've witnessed that very thing on a few occasions at the Springs. The Rangers/Sheriffs have escorted EVERYONE out of the Springs on more than one occasion.
I agree with an underlying premise you made: There's no [practical] way of screening people from entering public lands. The obvious exception to this rule is UNLESS they enter thru private property.
You say "everyone should be allowed access to DCHS". Well, maybe in theory. What would you say to terrorists who planned on starting forest fires near the Springs? Do they have this "right" also? I think your practical side would mandate that there's NO WAY you'd let them in, regardless of constitutionalities.
Some of us have just taken a more "liberal", and not-so-idealistic approach to this question and are not willing to wait for trouble to erupt before some action is taken. At least in theory this is the case. In reality, I'm pretty much content with paying my 4 bucks and watching what happens with the other routes into the Springs. Even if something were to happen as a result of someone coming in thru an uncontrolled point, about the only thing I'd do is say, "I told you so.".