In my case, I just applied for residency, had it granted, and I was waiting to receive my DNI. So, I didn't know my number. According to the woman at Hipolito Yrigoyen, I had to come there "sí o sí" because they can't see the DNI numbers in Retiro -- I can't imagine that, but that's what she said. In order to retrieve the DNI from Jujuy 468, you supposedly have to know your (DNI) number first.
My last question still stands, though: Can I travel abroad with just my DNI number, expired precaria (the only "official" documentation I have at this point) and my US passport? Does anyone know?