I guess it does sort of follow the original "white elephant" idea. Which, if I understand correctly, was that a white elephant was considered special and sacred, too special to allow to do work. And yet it needed to be fed, and elephants eat an enormous amount a day. So, basically, giving somebody a white elephant meant that they had to feed it and keep it alive (to do otherwise would be terrible, considering that it was a sacred creature), but they couldn't get any work out of it that would make it worth its keep. It was a gift that would destroy you and your family. I don't remember if the emperor didn't get that or if it was given deliberately to enemies.
That said, I think any sort of live animal is a horrible gift, and should never be given to anyone unless you *know* they want it *and* are happy to have you choose it. For instance, for your spouse or child. Basically in no other circumstance.