In my experience and what I hear about problems with Acceptance Driven Development (ATDD) practice, is that it's not easy to have the customer in the same room to create highest abstraction level Test Cases. This is of course a problem to business people and it might be a little bit hard to sell, if you don't have any experience of your own about the topic.
One of the easier way how a corporation can start to practice this is to try it out with internal customers. Usually there should be a situation where the whole product is not created in one place. These kind of relationships are eg. platform vs. application, where platform is created in one part of organization and application(s) in another. It's easier to create Test Cases and get people in the same meeting room when they are close to each others and there are no company barriers.
These activities aim to raise competence and good knowledge about practice inside the company. ATDD of course aims for communication with real customers, but this is a good way to get hands-on.