Susceptibility to the rubber hand illusion (RHI) varies. To date, however, there is no consensus explanation of this variability. Previous studies, focused on the role of multisensory integration, have searched for neural correlates of the illusion. But those studies have failed to identify a sufficient set of functionally specific neural correlates. Because some evidence suggests that frontal α power is one means of tracking neural instantiations of self, we hypothesized that the higher the frontal α power during the eyes-closed resting state, the more stable the self. As a corollary, we infer that the more stable the self, the less susceptible are participants to a blurring of boundaries-to feeling that the rubber hand belongs to them. Indeed, we found that frontal α amplitude oscillations negatively correlate with susceptibility. Moreover, since lower frequencies often modulate higher frequencies, we explored the possibility that this might be the case for the RHI. Indeed, some evidence suggests that high frontal α power observed in low-RHI participants is modulated by δ frequency oscillations. We conclude that while neural correlates of multisensory integration might be necessary for the RHI, sufficient explanation involves variable intrinsic neural activity that modulates how the brain responds to incompatible sensory stimuli.