ChatGPT did not make the treatment. ChatGPT summarized literature explaining how to make similar treatments, and then specialized tools were used to make the treatment. It is perfectly reasonable that ChatGPT can summarize literature and not make compliant 100 page legal documents.
The principle behind personalized mRNA vaccines is simple enough, and it's perfectly plausible that someone with money and lab access can create an effective treatment not offered through conventional means. It would be plausible even for a human patient right now, with mRNA vaccines still hung up in clinical trials. For a dog? Of course.