The Schottky barriers of transition metal silicides on silicon are characterized by two anomalous features, a face dependence of Schottky barrier heights (SBHs) and a weaker than expected dependence of SBHs on work function or "weaker Fermi level pinning." Density functional supercell calculations reported here find that these features arise from the occurrence of localized gap states at interfacial coordination defects, in addition to the usual metal-induced gap states (MIGSs), and these lead to pinning energies that increase sequentially across the Si gap from PtSi2 to YbSi2. The interfacial gap states vary in shape with face orientation and cause the unusual face-dependent SBHs. The localized interface defect states are a key missing addition to the MIGS model, which are needed to describe fully the interface bonding such as face orientation or coordination defects. This anomalous Fermi level pinning does not reduce gap state densities but could be used to better control SBHs by creating specific configurations with near band edge pinning energies, thus giving low contact resistances in highly scaled silicon devices or 2D semiconductors.