Hi Naners,
I think I know where your confusion lies....
Before my daughter was born, we decided to have her go on her father's insurance, because the cost to add her to mine was very high. The problem was that the coverage didn't start immediately, the coverage would start when she came home from hospital... because I am not on her father's insurance, the "newborn" hospital coverage would have to paid for by my insurance. When I called my health insurance to see if this would be covered, they said something along the lines of "oh yes newborns are covered by the mothers insurance automatically, but only until the newborn is released from the hospital following birth. If you want to cover her under your plan you have to fill out form xyz"
Your insurance would have only covered the baby automatically for the newborn hospital bills, but to keep the coverage you have to actually enroll... if the same rules apply.