"Actually, if it's fungal, then the Thing might not be able to assimilate it at all. It's already canon that the Thing can't assimilate plant cells. I see no reason why fungus cells would be different."
The comic "The Thing from another World: Climate of Fear". The whole comic takes place in a humid jungle, and MacCready mentions that if it could assimilate plant life, then the whole jungle should've been attacking them.