I believe it is called "Balance Billing". When an insurer pays a doctor for a provided service, the doctor accepts the insurance company's amount. For example, your child gets a vaccination. The doctor says it's $50. The insurance company says the standard payment for that vaccination is $40. They pay the doctor $40. The doctor is supposed to accept that, but sometimes they bill the patient for the other $10. It can happen at any time. If your friend has insurance, have her check to see if her insurance company paid for that visit in June 2010. And have her check to see if that pediatrician is in her insurance company's network.
If she is being billed for the amount the insurance didn't cover but that the doctor was supposed to accept, she can have her insurance company give her advice. You can look up "balance billing" and get more info, but make sure you do an advanced search on Google and only look for laws and regulations that are recent.
Most likely her visits weren't free, but were covered by insurance as part of the labor/delivery/maternity charges. So this may be the portion of the bill that the insurance did not deem reasonable.
If she went to an out-of-network pediatrician or doesn't have insurance, she probably has to pay that.
There is a time limit on how long after the service the provider can submit the bill to insurance. I don't know what the time limit is for "balance billing" the patient though.
I'm not an insurance person, by the way, or a medical person either, just a mom with a chronically ill child and a lot of paperwork and bills and three hospitals and 5 specialists and a million phone calls to the insurance company. So this is just my opinion, not professional advice by any means whatsoever!