The baby was infected, but this is a "functional cure", it works like this: Whilst in-utero the baby receives a certain amount of protection from the mother's immune system and the filtering of the placenta. When it's born it does have the virus, and then the baby's own immune system begins to kick in. At this point, immediately after birth, they begin an aggressive but fairly standard treatment with antiviral medication. This suppresses the virus enough that the immune system then has a fighting chance, and whilst the virus is unlikely to be completely eradicated it is in theory manageable by the immune system for the rest of the baby's life. The virus is still there, but kept to very low levels so developing AIDS or passing the virus on becomes very unlikely.
This approach may work with adults, but you have to get in there very quickly with the antivirals, so it's more likely to work with, for example, a nurse who gets a needlestick injury than a person who contracted it days before. The developing immune system in infants may also play a part, so this may never be a "functional cure" in adults, but it's certainly a step forward.
Remember, we don't necessarily need to cure things like HIV and cancer, we just need to keep them at bay until something else kills the patient, that still counts as a functional cure.