You still need something to show you are the parents, and most people use a birth certificate for that. A passport doesn't show who the parents are. If they accepted your with just an old passport, you got lucky as most times when they take the wrong document the passport office will send you a request for the correct documents to be sent in. Many of my friends have thought they were lucky that the post office or county clerk didn't take this or that document only to be contacted to send in more. Now most of us BEG the processing official to send in everything we have!
For my adopted child, I used her birth certificate to show I am her parent, but then used the old passport to prove she is a citizen. That is the only thing that made getting a new passport easier, as otherwise I have to use a certificate of citizenship and that's a pain (large document, always afraid it could be lost).
Nancy