So, being able to observe that one behaviour causes the desired outcome more often than another behaviour counts as reasoning using Bayes Theorem? On this level of vagueness we could proclaim children natural frequentists, or Popperian falsificationists, or whatever else with equal ease.
The children adjusted their hypotheses appropriately when they saw the statistical data
Using such words to describe small children trying to light up a toy makes me suspect that this post is a parody.
This recent article at Slate thinks so:
Why Your 4-Year-Old Is As Smart as Nate Silver
There also seems to be a reference to the Singularity Institute:
(Of course, I don't know how many other AI researchers are using Bayes Theorem, so the author also might not have the SI in mind)
If children really are natural Bayesians, then why and how do you think we change?