The thing is, in a democracy (actually in any form of government, but especially a democracy) I don't think you can cleanly separate those two things. When a sufficiently-large segment of the public decides X is a problem, then X is a problem, period. Even if X is objectively, truthfully, not a problem. And you can sit back and be satisfied that you have proven X is not a problem, but who cares? Your proof does not by itself affect the material state of the world one bit, where X will continue to be a problem.