The statistical arrangement of oriented segments in natural scenes was recently proposed to be indicative of a cocircularity rule. In particular, the probability density function of the relative position of two oriented segments was found to be maximal along fixed angles on the plane, consistent with the two segments being tangent to two points of a circle. Does this observation point to a prevalence of circles in natural scenes? Here we demonstrate that similar statistics can be obtained even when circles are not very common in visual scenes. The reason is that circles or near circular objects can heavily skew the distribution in favor of the cocircularity rule.