I mean, you could interpret that as "most cancer screenings don't extend life, because they come back negative". It's the "not most" case you're testing for in the first place.
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.