Does adjustment for non-differential misclassification of dichotomous exposure induce positive bias if there is no true association?

This article is a response to an off-the-record discussion that I had at an international meeting of epidemiologists more than decade ago. It centered on a concern, perhaps widely spread, that adjustment for exposure misclassification can induce a false positive result. I trace the possible history of this supposition and test it in a simulated case-control study under the assumption of non-differential misclassification of binary exposure, in which a Bayesian adjustment is applied. Probabilistic bias analysis is also briefly considered. The main conclusion is that adjustment for the presumed non-differential exposure misclassification of dichotomous does not "induce" positive associations, especially if the focus of the interpretation of the result is taken away from the point estimate. The misconception about positive bias induced by adjustment for exposure misclassification, if more clearly explained during the training of epidemiologists, may promote appropriate (and wider) use of the adjustment techniques. The simple message that can be derived from this paper is: "Exposure misclassification as a tractable problem that deserves much more attention than just a typical qualitative throw-away discussion".