Indeed, we do not know just accurate the stats are. The same thing happens in our world.
A person in our world, for instance, might be said to have an 'Age' stat. A person's age stat might be 22, when in reality they are 22.35321456843 years old.
Or, looking at it from the other side, There are only 5 stats we have been told about. Four here and Loyalty. Do those 5 (4 if Loyalty doesn't really exist as a stat) really determine all capabilities of a unit? Which determines Bogroll's skill at smithing and cooking? Obviously there are things not represented by those stats.
For that matter, we are told that the Duty natural thinkamancy requires Commanders to 'use our own initiative in the service of the Ruler.' What stat controls initiative & creativity?
I forgot about Conway's Life Game. Excellent example.