When several multistable displays are viewed simultaneously, their perception is synchronized, as they tend to be in the same perceptual state. Here, we investigated the possibility that perception may reflect embedded statistical knowledge of physical interaction between objects for specific combinations of displays and layouts. We used a novel display with two ambiguously rotating gears and an ambiguous walker-on-a-ball display. Both stimuli produce a physically congruent perception when an interaction is possible (i.e., gears counterrotate, and the ball rolls under the walker’s feet). Next, we gradually manipulated the stimuli to either introduce abrupt changes to the potential physical interaction between objects or keep it constant despite changes in the visual stimulus. We characterized the data using four different models that assumed (1) independence of perception of the stimulus, (2) dependence on the stimulus’s properties, (3) dependence on physical configuration alone, and (4) an interaction between stimulus properties and a physical configuration. We observed that for the ambiguous gears, the perception was correlated with the stimulus changes rather than with the possibility of physical interaction. The perception of walker-on-a-ball was independent of the stimulus but depended instead on whether participants responded about a relative motion of two objects (perception was biased towards physically congruent motion) or the absolute motion of the walker alone (perception was independent of the rotation of the ball). None of the two experiments supported the idea of embedded knowledge of physical interaction.