Have you looked into the literature surrounding maternally-derived antibodies? These are passed through breast milk and are thought to help prevent a variety of infections in newborns. Don't know if this has been documented for HIV specifically, but I wouldn't be surprised if this turned out to be the case.

I understand that the HIV virus can be transmitted to the baby through breastfeeding. If this is the case, HIV mothers are not to breast feed their babies. Am I correct?

Exclusive breastfeeding doesn't protect infants from acquiring HIV from their HIV-infected mothers. However, the benefits of breastfeeding in infants under 6 months (such as good nutrition and passive immunity against certain infectious diseases) outweigh the risks in developing countries. The WHO recommends breastfeeding where replacement feeding cannot be provided for children born to HIV-infected mothers.