Move fast and break things is a really unfortunate name. In my experience, the process of continous deployment, and the automation and defintion of processes to do it well bring more stability than the "move slow and keep things stable" environments. When you deploy once a month (or less!) you view deployment as a one off thing. When you deploy every day or every week. You view releases as a regular part of development. That change in mentality is critical to stable releases.