With direct flame on it? I guess it was removing water molecules slower than it was absorbing water. As long as it was saturated it would be fine. Great experiment.
There's also a great experiment with a normal baloon, keep a tiny bit of water in it and the you can hold the inflated balloon over a flame as long as the water doesn't boil away
the mechanism of it is not that paper is saturated with water, but that while there is water in the container, paper doesn't get hotter than 100C and a bit, not enough to ignite.
