I think it's fair to say that it's outright misleading - the water is not produced in any reasonable sense of the word.

I get how it may be misleading, and given that produced water should be in quotes to mark it as an industry term, it is still the only useful term for said water. Within the industry it is very well defined and easily understood. If you use another term like "obtained water" it would be up to interpretation by each individual including industry individuals. It's like contract law, they figured out a while ago that when dealing with technical issues, technical words should be used and taken to have their normal industry meaning, otherwise it breeds more confusion.