The rubber hand “illusion” (RHI), in which participants report experiences of ownership over a fake hand, appears to demonstrate that subjective ownership over one's body can be easily disrupted. It was recently shown that existing methods of controlling for suggestion effects in RHI responding are invalid. It was also shown that propensity to agree with RHI ownership statements is correlated with trait phenomenological control (response to imaginative suggestion). There is currently disagreement regarding the extent to which this relationship may cofound interpretation of RHI measures. Here we present the results of simulated experiments to demonstrate that a relationship between trait phenomenological control and RHI responding of the size reported would fundamentally change the way existing RHI results must be interpreted. Using real participant data, each simulated experiment used a sample biased in selection for trait phenomenological control. We find that using experiment samples comprised only of participants higher in trait phenomenological control almost guarantees that an experiment provides evidence consistent with RHI. By contrast, samples comprised of only participants lower in trait phenomenological control find evidence for RHI only around half the time - and of greater concern, evidence specifically for “ownership” experience just 4% of the time. These findings clearly contradict claims that the magnitude of relationship between phenomenological control and RHI responding is a minor concern, demonstrating that the presence of participants higher in trait phenomenological control in a given RHI experiment sample is critical for finding evidence consistent with RHI. Further study and theorising regarding RHI (and related effects) must take into account the role that trait phenomenological control plays in participant experience and responses during RHI experiments.