He wouldn't get anywhere, because the veterinary practice is well within their rights to withhold the animal and charge reasonable board until the customer pays.
Hey, no disrespect, you're obviously either a vet or friends with one and you've seen them taken advantage of by non-paying customers too often. I'm not implying that it's not a reasonable fee or that she shouldn't pay it, and I respect vets and the work they do, but I just question the legality of withholding the animal until the customer pays! If you're right and the vet is within his rights, then I dispute the morality of the law that allows them to do that.
I know it's an animal and doesn't have any rights per se, but surely it can't be put on the same ground morally as the mechanic refusing to return your car until you pay for the repair - it may be a possession, but it's a living thing, not an object.
There are many other ways for the vet to recover their money - small claims court, collection agencies, whatever. They don't need to effectively hold a small animal for ransom.