I think your probabilities are way off. We know that some people can smell some disease factors already (fetor hepaticus). Additionally, there's a LOT of gene

I think your probabilities are way off. We know that some people can smell some disease factors already (fetor hepaticus). Additionally, there's a LOT of genetic smell differences -- cilantro, cucumber, asparagus, cyanide, etc. Knowing these facts drastically affects both the P(smell) and P(skill) (which you've combined into P(skill)). Additionally, the likelihood that a particular person would be so convinced in their ability to smell Parkinson's that they sufficiently convince a few researchers AND THEN predict with perfect accuracy is much smaller than 1/4096. This isn't a random person picked off the street--this is a person specifically claiming to be able to accomplish a feat and then being successful on the first try at 1/4096 odds (1/2^12). Combined, I find this result very interesting and strongly believe the validity of this research. Granted, just because something is likely doesn't necessarily make it true, but it's certainly a strong impetus for future research, or even for people with a similar talent to come forward.