There is a beautiful story of a disagreement that Maimonides had with a philosopher. The philosopher claimed that he could change a cat and make him act like a person. Maimonides said this was impossible. They agreed to make a contest. When the day of the contest came, the philosopher brought a cat that he had trained to be a waiter. The cat served an entire meal, and the audience was amazed. Just as they stared and assumed that Maimonides had been proven wrong, Maimonides took out a container from his pocket. He opened it up and a mouse ran by. The cat saw the mouse, dropped the tray of dishes that he was holding, breaking them all, and ran after the mouse. Maimonides was proven right, and everyone agreed that no matter what, a cat is a cat. As much as he may be trained to act in a particular way, he is still inherently a cat and must be treated as such.
I find this story difficult to believe, given the claim of extremely high-level animal training that the Rambam's disputant was able to achieve. I find it hard to even picture a cat with the physical, much less mental, ability to serve a meal as a waiter would. It's particularly jarring to hear a story about the Rambam, in particular, that features apparently supernatural feats performed by random philosophers, given his own rationalist bent.
In addition, the punchline of this story is identical to that of a similar story in the ancient Greek story teller Aesop's Fables called "The Cat and Venus," which has been adapted in many forms in Western culture. It's plausible that this fable was adapted for Jewish audiences by replacing the Greek goddess in the title with a venerable Jewish figure and replacing the bedchamber in the fable, with the more modesty-friendly dining table.
Is there any other documentation of the provenance and veracity of this story?
If the story is not literally true, can the core principle expressed therein be traced to a particular teaching of the Rambam, or is there any other aspect of the story that can be associated with a documented element of the Rambam's teachings or life?