Most of your skull is solid, but if you look at a CT, the whole area around your eyes and nose is made up of air pockets (the sinuses) with distressingly thin walls between them. And bone is quite springy – I have here a bone folder*, about 200mm long and 4mm thick, and I can easily bend it by several millimeters.
We’re not talking about squeezing out the sinuses like ketchup packets though. I’m picturing something more like flexing the spout of a milk carton to allow it to drain more freely. The opening of your maxillary sinus is something like 2mm wide, minus the thickness of the (potentially inflamed) tissue lining it, so the difference between sealed and not sealed could be very small. I’m sure this kind of manipulation does move the soft tissue as well, but in any case, it’s not some outlandish idea with a heavy burden of proof.
If the sinuses were filled with really thick snot, it would take more than this to drain them, but then, if you have problem sinuses, your ostia probably aren’t wide enough for snot to get in there to begin with; it’s more likely to be tears, or even just air, that can leak out freely once you get the flow started.
* A thingy for folding paper, made (despite the rosy claims on several bookbinding sites) from the long bones of murdered cows
