The science direct link isn't working for me.
But here's the problem as I see it. Parkinsons has an occurrence rate in the population of 0.1%. If there are conditions which cause the same smells as Parkinsons and they are more common in the population (1%, 5%, 10%) then this test all the sudden becomes very not useful because even at 1% occurrence rate in the population it's already 10x more likely that you have that condition rather than Parkinsons. That's the confounding problem. And a different comment here pointed out there are conditions that also seem to have exhibited the same smells.
Who knows, perhaps this is still worth it, but for an n=30 study, this is basically nothing to consider. The group size is simply way too small.
BTW, Medical media reporters really should have a "No reporting on studies with n < 500" rule. These sensational studies are always preliminary on really low population groups. I'd love to see the meta analysis to know how many studies it's lumped in and how big those are, though.