Susceptibility to the rubber hand illusion (RHI) varies. Thus far, however, there is no consensus as regards how to explain this variation. Previous studies, focused on the role of multisensory integration, have searched for neural correlates of the illusion. Those studies, however, have failed to identify a sufficient set of functionally specific neural correlates. An alternative explanation of the illusion is that it results from demand characteristics, chiefly variability in the disposition to respond to imaginative suggestion: the degree to which intrinsic neural activity allows for a blurring of boundaries between self and external objects. Some evidence suggests that frontal alpha power is one means of tracking neural instantiations of self; therefore, we hypothesized that the higher the frontal alpha power during 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 alpha amplitude oscillations negatively correlate with susceptibility. Moreover, since alpha and delta oscillations seem to be associated in pathological states that allow for a blurring of boundaries between self and external objects, we conjectured that the high frontal alpha power observed in low-RHI participants is modulated by delta frequency oscillations. Indeed, we found this to be the case. Based on our findings we propose that the two explanatory frameworks might be complementary: that is, the neural correlates of multisensory integration might be necessary for the RHI, but a sufficient explanation requires investigation of variable intrinsic neural activity that acts to modulate how the brain responds to incompatible sensory stimuli.