It would not be first nor last made up story on these forums.
Right, you dastardly dimwit, to prove you wrong I've used up my lunch brake to do some !!Science!! (much to the horror of the dwarven merchants).
Creating a new world from scratch, on an unmodded phoebus DF install, I waited for three seasons until the first dwarven caravan. Then crushing a part of the carts with a small bridge, I had access to a caged sow.
I first designated it to be melted, then unforbid it. Then I set the task in the smelter to melt metal objects. My smith then promptly went up to the surface, dragged down the unfortunate sow, and stuffed it and its cage into the smelter.
The sow never reappeared. It was also added to the list of the dead.
I now have this world saved, and I'm confident that this can be replicated by anyone.
I can now say confidently, that you can certainly smelt caged animals that have been unforbidded after the death of dwarven merchants. More science should be done though to determine whether this only occurs to animals brought by dwarven merchants, or if it can happen to unforbidden animals as well.
Unfortunately, having used up my lunch, I've now got to get some proper (although less amusing) work done!