A couple of things. First, the cancer thing. If you have a hereditary history of cancer, you are more likely to get cancer, and that is usually the case in certain types of cancer, like breast cancer, colon cancer, etc. Other cancers, lung for example, rarely happen to someone who doesn't use any tobacco products. So its a whole host of factors. Doesn't really matter though, you'd think by the 27th century they'd have a cure for cancer.
Two, the Native Americans didn't have any diseases thing. Um, I wish there was a more polite way to say this, but that's just wrong. Miserably wrong. The Europeans DID bring diseases to America with them, most notably smallpox, that devastated the Native American communities due to the fact that the Native Americans had no inborn defenses against the disease that only comes from a society being exposed to it for a long long time. The Europeans brought other diseases back with, most notably syphillis, as was stated earlier in the post.
Bassman (the a in bass is long, I don't fish)