score:2
You ask: What did Jesus do regarding the Jews believing that some diseases were sometimes due to sin?
There's one passage in particular where explicitly corrects the disciples regarding a man born blind in John 9:
As he passed by, he saw a man blind from birth. 2 And his disciples asked him, βRabbi, who sinned, this man or his parents, that he was born blind?β 3 Jesus answered, "It was not that this man sinned, or his parents, but that the works of God might be displayed in him."
Admittedly, Jesus may not go as far as addressing the scientific causes of this "disease" (I'm not aware of any teaching of Jesus along those lines), and the inference to the "disease" being a result of the Fall is weak at best. Nonetheless, he does clearly teach that a) the disease was under God's sovereignty and b) the disease was not due to the man's sin.