Well, you've reduced a rational position to absurdity here. The concern isn't that someone is going to require chemotherapy. The concern is that an asymptomatic condition will go undisclosed until it is symptomatic, at which point preventative treatments are futile.

Even if we accepted your example, there is a fundamental inconsistency, since doctors in America regularly prescribe very serious drug interventions for patients who essentially self-diagnose for being neurotic/adhd/etc.--actually a much worse problem than the one you're so eager to curtail.