This article mentions that Aspergillus can cause sinusitis. One reason that Aspergillus and other airborne micro-organisms can infect sinuses is that there are air channels leading from the nose directly into the sinuses - partly to provide a natural drainage channel for mucus. Aspergillus spores (seed-like particles) are so small and light they float freely in the least puff of air, so accessing nasal passages and chambers filled with air branching off the nasal passages e.g. the sinus' is quite easy. Taken together with the fact that all of us breathe in Aspergillus spores every day it is not hard to conclude that infection is not prevented by lack of supply of spores!
For the most part our natural defences against infection destroy spores quickly and efficiently - there are movies of precisely that happening in the Educational section of the Aspergillus Website.
Another 'mechanism' of preventing fungal growth in the sinus' that has some speculative merit stems from the observation that there is very little available zinc in the cavity. Fungi such as Aspergillus need zinc to grow, so the absence of zinc prevents fungal growth.
Zinc is plentiful in the material used to fill teeth and a little known fact is that that material can protrude right through a root canal filling into the maxillary sinus. There are two papers (1, 2) which discuss cases of root canal amalgam protruding into the sinus which are covered with fungal growth within the sinus, consistent with the amalgam aiding growth as described above.
We should emphasise that this is an incredibly rare phenomenum - there is no need to question your dentist on his technique just yet, except perhaps to remind him/her not to overfill!