We present direct evidence of enhanced Ga interdiffusion in InAs free-standing nanowires grown at moderate temperatures by molecular beam epitaxy on GaAs (111)B. Scanning electron microscopy together with X-ray diffraction measurements in coplanar and grazing incidence geometries show that nominally grown InAs NWs are actually made of In$_{0.86}$Ga$_{0.14}$As. Unlike typical vapor-liquid-solid growth, these nanowires are formed by diffusion-induced growth combined with strong interdiffusion from substrate material. Based on the experimental results, a simple nanowire growth model accounting for the Ga interdiffusion is also presented. This growth model could be generally applicable to the molecular beam heteroepitaxy of III-V nanowires.