As a point of interest, a lot of airlines forbid their staff to carry infants/toddlers for the reason of liability in the event of an accident (eg baby is dropped), instead we are trained to relieve the parent of the bags and other stuff so that the person can focus on carrying the baby( I'm guessing the case here did not involve carrying the baby). Not sure if the airline can still deny liability as any good lawyer will be able to contest this.
Having said that it is a human reaction to offer to carry the baby and I've seen the rule frequently broken.
Anilv