What legal obligation did google have to out the blogger, Rosemary Port?

Defamation is illegal and the court found that the model had a reasonable claim of defamation and was entitled to know the identity of the blogger. It's perfectly legal for a court to order a company to provide information in discovery and a company that refuses to follow a court order faces fines and contempt orders. She has no chance of winning a dime in her case against Google. It was following a lawful court order.