The experimental task involved adults and children seeing a picture, then having part of the picture blocked and trying to guess what a naive observer would think was in the blocked section. Children get better at this as they get older, but this is mediated by working memory improvements, and differences between individuals are mediated both by inhibitory control as well as working memory. This is in accord with previous work on modeling others' (false) beliefs in general.
Hansen Lagattuta K, Sayfan L, Harvey C. Beliefs About Thought Probability: Evidence for Persistent Errors in Mindreading and Links to Executive Control. Child Development, ahead of press 2013, Volume 00, Number 0, Pages 1