OK, let's review.
When you heat water in paper, the water cools the paper below the waterline, allowing it continue to exist. This is possible not becuase paper is porus (you can, but shouldn't, do this in clayed paper) but becuase it doesn't melt.
Nalgene bottles melt. You have no way of acurately knowing how hot your drop rock is- 310-ish, you have a leaky bottle. Even if you could realiably determine the temperature of the rocks, it would be horribly inefficent. The difference of tempurature between 212 and 280 (safety margin) is relatively small when figured as energy (watts, newtons, whatever makes your hair stand up), and you would only be able to raise the tempurature of a very small mass of water with a stone. Sure, you could keep adding stones, but at that point you are basically pouring a mass of gravel into your water bottle. A comparitively large mass of heated gravel- you'd have more stones than water.
That ignores the long term exposure issues that lexan has to tempuratures over 240, IIRC. Water can not, at normal pressures, get above 212 degrees, so that's safe. But there is no way I can think of the boil water in a lexan vessel safely.
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-IronRaven
When a man dare not speak without malice for fear of giving insult, that is when truth starts to die. Truth is the truest freedom.