That makes no sense at all, unless you're saying that people should respond to all such information by ignoring it.
There's plenty of room between "go under the knife" and "ignore altogether."
Getting a test good enough to still make it useful (detect enough of the true positives) would of course be a challenge, but the more data is available, the more feasible that might be.
if someone told you, you had a .01% chance of getting a disease for example, aren't you better off with that information? even if it is noisy?