I meant in the second example. I agree that in the first one if she doesn't use the desire as evidence of the gene she'll get a result saying she should smoke. But in the second one even if she does ignore that then the probability of cancer given that she smokes is higher than the probability of cancer given that she doesn't.

If she doesn't have the gene, then she can smoke or not without any change in risk. She doesn't know if she has the gene or not, but if she then smoking makes her more likely to get cancer. So, if she sums across both possibilities, she's more likely to get cancer if she smokes. Not by as large a margin as if she knew she had the gene, or even by as large a margin as she would estimate if she included the urge to smoke as evidence that she does, but it's still more likely.

P(C|S&~G) = P(C|~S&~G) = P(C|~S&G) < P(C|S&G). So P(C|S) > P(C|~S), even without looking at the probability of the gene given that she prefers to smoke.