In this paper, we show that many formal and informal security results on distance-bounding (DB) protocols are incorrect/incomplete. We identify that this inadequacy stems from the fact that the pseudorandom function (PRF) assumption alone, invoked in many security claims, is insufficient. To this end, we identify two distinct shortcomings of invoking the PRF assumption alone: one leads to distance-fraud attacks, whilst the other opens for man-in-the-middle (MiM) attacks. First, we describe –in a more unitary, formal fashion– why assuming that a family of functions classically used inside DB protocols is solely a PRF is unsatisfactory and what generic security flaws this leads to. Then, we present concrete constructions that disprove the PRF-based claimed security of several DB protocols in the literature; this is achieved by using some PRF programming techniques. Whilst our examples may be considered contrived, the overall message is clear: the PRF assumption should be strengthened in order to attain security against distance-fraud and MiM attacks in distance-bounding protocols!