There are high hopes that clinical decisions can be improved by adopting algorithms trained to estimate the likelihood that a patient suffers a condition C. Introducing work on the epistemic value of purely statistical evidence in legal epistemology I show that a certain type of AI devices for making medical decisions about persons rely on purely statistical evidence and that it raises an important question about the appropriateness of relying on such devices for allocating health resources. If the argument I present is sound, then it suggests a radical rethinking of the use of prevalent types of AI devices as well as the use of statistical evidence in medical practice more generally.