Frankly nobody who actually knows much about mycology and mold would from looking at the white growth on a surface by naked eye assert that it is a species of aspergillus.
Fungus on roof rafters.
It is not necessary to remove all stains from wood.
Attic mold is often caused by warm moist air from the house leaking into the attic space.
Left unattended the moisture and fungal growth will eventually degrade the roof sheathing.
Roof leaks will often lead to a small localized area of attic mold near where the leak is occurring.
With biannual professional inspections you can identify such problems before they impact the structural integrity of your roof and the sanitation of your house.
This causes condensation to form on the cold surfaces in the attic especially roof rafters sheathing and trusses.
The mold will simply grow on top of and through the layer of paint.
That could indeed be and looks like a white fungus or mold growth on roof sheathing.
Painting or sealing it will not address the problem.
Fungal spores hyphae and conidiophores the spore producing structures of mold.
Below are a few ways to check for possible roof leaks.
Rafters sheathing joists attic side of fascia boards etc.
You must address the underlying moisture issue in order to stop the mold growth.
Therefore we already know something about your third remediator and his or her claim.