We identify common hypotheses on which a large number of distinct mathematical models of WLANs employing IEEE 802.11 are founded. Using data from an experimental test bed and packet-level ns-2 simulations, we investigate the veracity of these hypotheses. We demonstrate that several of these assumptions are inaccurate and/or inappropriate. We consider hypotheses used in the modeling of saturated and unsaturated 802.11 infrastructure mode networks, saturated 802.11e networks, and saturated and unsaturated 802.11s mesh networks. In infrastructure mode networks, we find that even for small numbers of stations, common hypotheses hold true for saturated stations and also for unsaturated stations with small buffers. However, despite their widespread adoption, common assumptions used to incorporate station buffers are erroneous. This raises questions about the predictive power of all models based on these hypotheses. For saturated 802.11e models that treat differences in arbitration interframe space (AIFS), we find that the two fundamental hypotheses are reasonable. For 802.11s mesh networks, we find that assumptions are appropriate only if stations are lightly loaded and are highly inappropriate if they are saturated. In identifying these flawed suppositions, this work identifies areas where mathematical models need to be revisited and revised if they are to be used with confidence by protocol designers and WLAN network planners.