So much this. The smoothest integration I've ever worked on was one where I owned the API and back-end and another team built the front end. I defined the API behaviors, built the tests verify those behaviors, and created a mock API for the front-end folks to use while testing.
Over the course of building the API, I slowly got my test success rate from 0% to 100% and always immediately knew when I accidentally changed behaviors. When we finally integrated, there were literally 0 errors related to the client/server interface. Yes, there was some UI wonkiness and we discovered some issues of scale, but there were no issues with parameter values, HTTP response codes, error messages, etc. It was a) amazing and b) the only time I've had the luxury to build something in that manner.