100% with the airline on this one. The kid had headlice. They would have spread on the plane and the seat. Pretty soon that could have become an infestation. Plenty more people could have been infected and pretty soon it would have been traced back to Delta and then the media ****storm would have hit back at them for not cleaning planes properly etc.
However, that said, there must be hundreds of planes out there spreading lice around from unsuspecting passengers. Perhaps a high profile headlice case would lead to improved cleaning standards industry wide...but then again, the media ****storm would then be on the "deadly chemicals used to clean planes".