BUT I don't think fungi produce sugars do they? So as mushrooms are a fungi, there are no sugars in them to make into alcohol.
It's mostly that fungi produce sugars in such a form that the yeast can't use 'em. It's the mushroom equivalent of chitin, I believe, they make the cell walls out of it.
They have to have some form of glucose for cellular respiration, but I don't believe fungi make starches. they either don't store sugar at all or they store it as long tendrils of extremely resilient substance.
Because of this, edible mushrooms are really low in calories, so the thing that makes them great as an additive in one's diet for vitamins and nutrients and amino acids (esp. if vegetarian of some sort) makes them horrible for brewing.
Part of me imagines that either dwarves have a process for breaking down the chitin (just checked wikipedia, the cellwalls are actually called chitin or are another polysaccharide) or plump helmets are the sugar beets of the fungal world, in that they store a large amount of starch/sugar in their bodies. Possibly to tempt...
Oh my god. Plump helmets are actually parasites. They're full of sugar so that the dwarves eat them. Then they get into the body of the dwarves... The Plump helmet parasites as a potential source of strange moods!?
Dwarves being dwarves though, don't always eat them, sometimes they brew them into alcohol so that the parasitic effects are haphazard.
As for getting more than spatters of alcohol by cutting open a plump helmet man, I'm having the horrible image of a dwarf drowning in 4/7 plump helmet blood-wine after wrestling and eating open a pack/herd of plump helmet men. A contented smile on his beard.