Please think carefully about having your vet document anything, as it can be used against you.

If the cat were a gift (and really, the only way you would have 'rights' to it is if it were a gift, otherwise, you are just the person caring for the cat (think of a car parking lot...you leave your car there, under the care of the attendant, but it is still your car, presuming you pay the money to park there)), there isn't any reason to document that the cat should stay with you, for medical reasons or any other reason.

If a cat is MINE, my vet doesn't need to document why my home is better than someone elses' home. It is the ONLY home.

If a cat is NOT mine, but I want it to be mine, then, I would need to document that my home is a better home than someone elses'. That opens the door to the belief that maybe the cat isn't yours after all.

I would document nothing, and say nothing to anyone, other than, "I have no idea what she is talking about! My goodness, she gave us this cat 8 months ago! Like we would ever give it up now?".