'Into the Woods'?

Anybody besides me wonder whether James Lapine, who wrote the book for Sondheim's "Into the Woods," must have seen this movie as a child? Jack mistakes his (obviously female) cow for a boy and has a moving goodbye scene with the animal, after which the cow cries... all of which appeared in "Into the Woods." This seems too much to be coincidence. Lapine would have been six years old at the time this film was released, exactly the age to have taken it all in but not remembered it later.

No way to know for sure, I suppose. But still, I wonder.