One piece of evidence in support: The local Children's Museum does not allow adults to enter if they are not with a child. The adult:child ratio is approximately 1:1.5. Further, I've never been more than ten feet from my son when visiting - and I estimate I'm within one standard deviation of the norm (it's hard to tell, in part because children from 2-8 are there, and the distance-to-child norm varies naturally by age) In short, there is no reasonable likelihood of stranger abduction.
Yet the policy is in place - a response to fear mongering, as far as I can tell.