I was originally going to speculate that it was due to the TSA security era, but it appears to be an international issue: http://www.flights.com/faq.html#18
ETA: The wording was so identical in so many places that I suspected it was old; I now think the issue is coming from the Hague Convention of 25 October 1980 on the Civil Aspects of International Child Abduction. The Best Practices document for that has a lot about (non-legally-binding-but-still-really-suggested) prevention of kidnappings before the (slightly more legally binding) agreements to work with other countries to make sure kids get returned. Though I could not find anything explicitly talking about different last names.
no subject
http://www.flights.com/faq.html#18
ETA: The wording was so identical in so many places that I suspected it was old; I now think the issue is coming from the Hague Convention of 25 October 1980 on the Civil Aspects of International Child Abduction. The Best Practices document for that has a lot about (non-legally-binding-but-still-really-suggested) prevention of kidnappings before the (slightly more legally binding) agreements to work with other countries to make sure kids get returned. Though I could not find anything explicitly talking about different last names.