Firstly, I'm only commenting on Australasian zoos. I'm sure there's all sorts of other practices in other regions. A number of US zoos feed monkey chow exclusively to some of their primates. These look like large chicken feed pellets, and supposedly contain a balanced diet. I don't think any of the major zoos in this region use these diets for primates.
Just a minor clarification - if a single keeper (and I think's that's what you are referring to), complained bitterly about a particular diet, then yes, I would agree, the general management response would be some sort of discussion and/or resolution. In most of the major zoos (I don't know about the smaller zoos though), animal diets are developed by the veterinarians, in conjunction with curatorial staff, and based on species requirements and available foodstuffs. Sometimes, complete substitutes for wild diets are made - echidnas are not fed 1,000s of termites every day, but rather a mix of meat, eggs, mealworms, and all sorts of other goodies that replicate the dietary needs of an animal.
Substitutes (calcium powder and vitamins) are often added to large cat diets on the days when meat is fed, but this still isn't a complete substitute for carcases.