The way i have seen it used was more like the inverse of your first example, where one go from encoded and tested sysadmin tasks to "lets throw into production any newfangled thing the devs (monkeys hammering keyboards, more like it) wants to use".
But there's more to it... sometimes the engineering work it takes to prevent something from crashing is much less than just monitoring and restarting when failures are detected. Maybe "failure engineering" is a good term for a lot of the value Devops techniques can bring to a team?