I would say that this guy at the hut was plain wrong.
As far as I'm concerned, the working principle of the Gore-Tex membrane is gradient-driven. That means, the membrane itself (if you consider only the membrane and ignore the layers it is sandwitched in) does not have any physical or chemical preference to transport moisture into a certain direction. Instead it is built in a way, that
- water cannot pass it while vapour can and
- the vapour is pushed through the membrane by a difference in vapour pressure between its in- and outside, i.e. a combination of temperature and moisture difference.
Therefore what is "inside" and "outside" to the membrane is basically defined by the local conditions on both its sides. That does also mean, that reversing the conditions – i.e. drying the inside of the boot while the leather or fabric on its outside is still wet – could make the membrane work in the opposite direction and dry the outside through the membrane and the inner fabric. That would in the worst case increase the time needed to dry your shoes but not damage the membrane. Even if you consider other breathable fabrics, where the fabric itself contains a physical-chemical preference to transport water vapour into a certain direction (Sympatex for example), those will not get physically damaged when moisture is driven through in the "wrong" direction, it just takes more "force", i.e. a higher gradient to do so. For both membrane types, to really harm their function, you have to physically work them by repeated mechanical strain.
In addition, I doubt that a newspaper is able to create a strong enough vapour pressure gradient to "suck" the moisture from the boot's outside through the membrane to the inside. So I'm quite sure that your idea of the newspaper only drying the inside is correct.
But you should of course after some time remove or replace the wet newspaper from the inside. Otherwise you won't have won anything since the paper sucked the moisture from the boot but then kept a neat little atmosphere of dampness in the shoes which is the best way to make all kinds of bacteria feel well in there and make it a place of permanent bad smell...