I think you are confusing a child's abilities (of which they have no knowledge) with our knowledge of these abilities.
If a baby is able to predict above chance how her mother will respond under a repeated circumstance
we know this by giving meaning to a child's action, an hypothesis, and doing experiments to test/analyze this meaning.
http://www.alisongopnik.com/Papers_Alison/gopnik & seiver 2009.pdf
Alison Gopnik's mistake like most scientists and yours is to now ignore the semantics/meaning she invented to do the test and claim the syntax/rules she discovered is primary and proves the semantics/meaning always had to be there.
Once again the test of knowledge is whether small children are able to communicate the meaning of this ability to us.