Testing cultural knowledge is a perfectly valid thing to do.
I agree - but I believe we should do so in a way which is fair to all of the children being tested.
In the example I gave, it was not fair to ask the children of Asian ethnic origin about Anglo Saxon nursery rhymes - they weren't sung to them by their parents and aren't on any school's required curriculum. It is not fair they be expected to know them.
Similarly, in the studies cited of SAT'S, unfair weighting has been identified, which is to the disadvantage of children from a particular ethnic background.
By all means, test culture. Teach it, learn it, embrace it. But if we are testing it in a way which is unfair to an ethnic grouping, then we aren't doing it well.
Could there be any greater conceit, than for someone to believe that the universe has to be simple enough for them to be able to understand it ?