No, Flipper's reference makes sense in context. Modern popular culture has a great definition of unicorns. The point being, you can define something that doesn't actually exist quite well. Unfortunately nothing like them exists or has ever existed.
If there is an animal that was the basis for unicorn legends, it was likely this (An extinct rhino called Elasmotherium) The size and shape of the horn has to be inferred from the skull since rhino horns are not bony and do not preserve well (though there is a huge bony base where a horn would presumably be):
Sidenote: The hebrew word found in the old testament, re’em sometimes translated as "Unicorn", probably referred to aurochs, the wild progenitors of modern cattle based on a similar word in Assyrian.