I think too many people listen to the old wives tales
thankfully she seemed positive in her response and she right, many cats do adjust to children or it they're anything like mine when a child happens to visit, they just steer clear
I heard that a cat possibly sits on the baby, due to its baby smells (probably warmth too lol) and the smell of milk and they sit on them to protect them, like they would have the kittens all snuggled in. How true this is, is anyones guess - but i repeat it to people as if it were fact just to disspell this myth that cats somehow evil and are setting out on some sort of baby culling spree by smothering them all
like you said in your reply, you just shut the door to the babys room/cot and its being a reponsible owner and parent