"Any changes made to the terms should be known, understood, and agreed on by whoever sets the overall strategy for the product. The legal team helps them encode it, marketing and PR help them communicate it outwards"
That's actually the sort of compartmentalization that creates these problems. "Whoever sets the overall strategy for the product" = the head of Product or the Product Manager for a specific feature. This person rarely has any legal or communications experience. If the legal team's job is just to "encode" what product wants, then that's actually where the problem starts.
The only real solution here is for Product, Legal and Communications to work together from the beginning. The product feature should be designed with Legal and Comm concerns in mind. Otherwise, the danger is that you'll end up exposed to exactly the sort of snafu that Instagram experienced here.