That's a very irresponsible parent really. It was her responsibility to look after her baby, which she failed to do.
However, I don't get why a ton of people blame Facebook. She could just as easily been addicted to your favorite game on the Wii, watching TV, doing business work, playing Minecraft or looking at anime on Youtube. Hell, she could have been browsing GBATemp. It's not Facebook's fault, it's hers. It's ignorant to blame this on Facebook. It's just as unjustified if she was doing anything else instead of taking care of her baby, it's her fault, not what she's doing.