Hashem created the body and made disease. He also created man with a mind and wisdom and gave him permission to practice medicine (Ve’rapo yerapeh, ???? ???? Mishpatim, 21:19). Hashem created medicinal plants and antibiotics. Hashem made smallpox and cowpox, which essentially was the first (unintentional) vaccine. We are not outsmarting G-d, but fulfilling His Will.
Re the original quote, I don’t know what study shows that getting measles gives some sort of immunity to cancer, but I think it is more logical to conclude that these diseases protected against cancer, because once-upon-a-time people died young of bacterial infections and viral diseases before they could develop cancer!