[Hank Parsons]

It seems clear that the game doesn't re-roll an 'illegal' stat, but rather shifts the value to the closest legal value. That's why classes with high minimums have higher average stat rolls. All rolls falling beneath the minimum were automatically boosted up, without any affect on the other-stats' rolls. If you rolled low on stats with minimums, and you rolled high on stats that can be anything 3-18, then you'll have overall more high value stats.