Yes, it's true!
"That's Not Baby Talk It's Your Kid Testing Her Grasp of Chinese "
Sharon Begley. Wall Street Journal. Aug 11, 2006. pg. A.7
Not much to post, since the WSJ isn't free online, but here's the lead paragraph:
"IF A BABY GROWING up in an English-speaking home squeals 'a my pencil!' dad might correct him, saying, 'That's "my pencil," sweetie.' If a toddler points to an older brother and complains, 'tickled me,' mom might say, 'You mean, "Joey tickled me." ' And the toddler who declares, 'I don't want no spinach,' is told to say, 'I don't want any spinach.' "
A newly-appointed University of Pennsylvania linguist, Charles Yang, argues that these kids are actually speaking perfect grammar *of another language*. In his new book called The infinite gift : how children learn and unlearn the languages of the world he writes that "Children's language differs from ours not only because they occasionally speak imperfect English but because they speak perfect Chinese" (according to the WSJ) -- and this is consistent with Noam Chomsky's theory of universal grammar.
(thanks to Ross Buck for the article)