The smallpox 'argument'

Darian appeared on Radio 3's Night Waves yesterday evening. He was discussing the book with a sympathetic clinical geneticist and an antipathetic neurophysiologist. The latter brought up the case of smallpox again, in a very similar way to Theodore Dalrymple in his review mentioned four posts ago. I struggle to understand this argument but let me give it my best shot:

Premise: Psychotherapy can't cure smallpox
Premise: If there exists a disease which psychotherapy can't cure, no psychological factors are relevant to any disease.

Conclusion: No psychological factors are relevant to any disease.

Can that be it? How could they justify the second premise? Besides the curious jump from one disease to all diseases, they must hold something like:

Premise: If psychological factors are relevant to a disease, then psychotherapy should be able to cure it.

Now how far is this from expecting that after a lighted match has set off an explosion of gas, that blowing out the match will undo the effects of the explosion?

An only slightly less unreasonable smallpox argument would be:

Premise: No psychological factors are relevant to smallpox
Premise: If there exists a disease to which no psychosocial factors are relevant, no psychological factors are relevant to any disease.

Conclusion: No psychological factors are relevant to any disease.

Still a bad argument. We could show that all Cambodians are wholly evil, if we allowed 'If there exists a wholly evil Cambodian, then all Cambodians are wholly evil', and 'Pol Pot was wholly evil'.

But even here there would be some small scope for attack on the first premise. The work of Davidson on meditation and flu vaccine, I mentioned four posts ago, shows how an immune response is affected by mental state.