Pudel is German for poodle. It could be that an English speaker misinterpreted it as puddle. Maybe poodle, puddle, and Pudel were all spelled the same way because back then, spelling was a suggestion at best.
You can’t prove that a dog can’t shapeshift, only that it’s not currently shapeshifting. Maybe it can but doesn’t want to 
You can prove that a dog isn’t bulletproof simply by shooting it.
