I have never understood why anyone would say such a thing at an airport, the authorities are never going to find it funny. It also gives the impression to the security people that they are not being taken seriously. That's where the crux of the problem lies. The cop has then reacted in an appropriate manner but in their attempt to stop this happening again they are making an example of her.
Guys, you will never stop people making remarks like this, the public are just too stupid to learn not to.
I think this reaction stinks. If they realy want to punish her why not just deport her with the promise that she may never return to the U.S.A.