I have heard that, due to the tempermental weather in the White Mountains of NH, it is illegal to turn anybody away from the huts there. First of all, is this true? And secondly, what does it mean in practice? For instance, if I show up and say I don't have any money/a reservation, will they let me stay?

I maybe should mention that I'm a thru-hiker, and I don't necessarily plan to be one of the first two hikers to arrive to get work-for-stay, and I'm certainly not willing to pay the ridiculously high fees.