He's not denying that the conditions exist. What he is denying is that they are illnesses. A more accurate term would be injury.
http://www.sciencedaily.com/releases/2012/08/120816170400.htmDoes a viral infection count as illness or injury?
(Note the numbers are very significant here: 10-20% of people carry the T. Gondii infection. People with T. Gondii infection are 7 times more likely to attempt suicide. -> 60% or more of suicide attempts could be T. Gondii-related).
Alternatively, perhaps the axioms of natural law dictate that T. Gondii is either (a) caused by child abuse or (b) imaginary. Ask the cult leader for the correct answer. Interpretations of natural law at this level are quite subtle.
Or perhaps cat ownership is child abuse?
http://healthland.time.com/2012/07/03/are-cat-ladies-more-likely-to-attempt-suicide/(In the mouse, infection causes a loss of cat aversion. Maybe a strong infection could turn you into a upstanding Statist? Keep your girls clear of the cat litter Myrkul.)