Munchausen syndrome by proxy

I was watching this special on 48 hours about this condition, I had heard of it before but did not realize there was a name for it. People who have this condition obviously have a mental illness but I'm genuinely curious, for these people, if they were to have a chronically ill child or one that was born with special needs, would the condition manifest? I guess the way I understand it is that they do it for attention or to feel like the child needs them so if the child truly has a condition that requires more of there attention would they let it be or would they still feel a need to make the child even more sick? I can't relate because I can't stand to see my babies sick but for people who do suffer from this disease I just wonder if that would have any impact on their behavior. The poor child on the show passed away because of high sodium levels and the mother was sentenced to prison time denying that she had anything to do with the death of the child so it was a very sad story for all parties.