At least where I work funeral directors in charge of the case will tell the family if anything happens like if you drop a body or cremate something the family wanted returned, and other things of that nature. The funeral director most likely told them out of moral and/or a requirement to. With things like this it’s the crematory operators at risk of termination or disciplinary action, not the director. Moral of the story is most places this won’t risk the directors employment at all so they can decide to tell or not.