The researcher fails to address the possibility that the correlation between sleep deprivation and getting sick less often is due to another factor— like diet or exercise— that causally contributes to both.

The researcher never assumes that sleep deprivation is the only thing that prevents illness. Instead, she fails to consider that a given factor (sleep deprivation) might not causally contribute to the occurrence of a given phenomenon at all.

The researcher concludes that sleep deprivation strengthens the immune system from the claim that the two are correlated. She does not conclude that sleep deprivation exists from the claim that it is sufficient for a strengthened immune system.

Actually, the researcher takes for granted (or assumes) that one phenomenon causally contributes to the other since there is an observable correlation between the two phenomena.

The researcher doesn't claim that sleep deprivation is not associated with illness, just that it's associated less frequently than sleeping 8 hours. She also never assumes that sleep deprivation has no other negative consequences.