I've met a lot of people with degrees that "felt" they were good programmers, admins, whatever. For straightforward work they were good, but for poop-hit-the-propeller situations or ones that required imagination they actually performed rather poorly.
On the other hand, those with "life experience" were good in high-stress situations and worked well as creative thinkers, but were often fairly horrible at stuff like code structure, documentation, and time management of multiple tasks.
In many cases, schooling doesn't teach you to be a good worker. People who can read books and pass tests may be good for drone-work but not for many real-life situations. Alternately, there are critical skills learned in school which often make those people work better in an environment where they interact with others.
Most of the real rockstars/aces I've met aren't formally trained. They're highly skilled, driven, but often also cowboys who don't work so well with others (or produce work that can be read by others). Who you hire depends on what you need: formal structure, team player, or quick get-it-done ACE. In larger groups, usually having one of the aces is good for when unexpected stuff crops up, but having the formally trained guys/gals is also important for building a structure where you'll get less of the "oh sh*t" moments.