Not all positive tests are cancer. In some cases, actual cancers could be a tiny minority of positive tests. The tests themselves are a dangerous tool, and the way we minimize that danger is through statistics.
Then you are just changing one form of bad communication with another form. When a test indicates that there is cancer, the physician is not supposed to say "you have cancer" but rather "there is X% probability that you have cancer." If the test comes back negative, it should be "there is Y% probability that you have cancer" where presumably Y<X.