I agree that the fact it's caused by a fungus does not disqualify it from being a disease. I would have no problem saying paladins are immune to thrush, ringworm, and athlete's foot, all of which are caused by fungi.Speaking as a health care professional and former biologist - this is completely wrong. Disease is by far the more broad and encompassing term. ALL infections that cause impairment of the host organism are "diseases" (or result in diseases; the technical labels of the two may differ). Not all diseases are caused by infection (e.g. heart disease).
The paladin should be immune.
That said... given the mechanics, I think it's pretty clear the victim of the treant's attack is not the host for this fungus. If that were the case, the fungus would continue inflicting Dex loss over time. Instead it causes a bunch of Dex loss in 1 round and then stops. The fungus's host is the treant; an infusion of blood from a wound allows it to grow rapidly, but it can't keep growing away from the treant. This is really more of a physical attack than an infection.