(See, e.g., Einstein displaying knowledge of quantum mechanics without actually believing it, or assorted creationists who actually understand evolution.)
I think your claim that criminality is the best measure of knowledge is interesting. Among other things, it suggests that the best way to increase knowledge might be to shut down the education system and implement a police state. (For the cost of the current education system we could increase the number of cops/courts/prisons by a factor of 6.)
Actually, an easier way to reduce the crime rate to zero is to repeal all categories of crime. Make it legal to steal and murder. Then all you have are existential crimes: "How could you let this happen!?" types: where crime is a metaphor rather than a fact.
> (For the cost of the current education system we could increase the number of cops/courts/prisons by a factor of 6.)
Citation needed.
http://www.usgovernmentspending.com/piechart_2010_US_total
We spend a lot on education, not so much on cops.
Education is a way of ensuring a more advanced and productive society through imparting certain knowledge and ideas to its children. The best metric for measuring the performance of an education system is rates of criminality. If a society has high crime rates then its education system is failing to produce productive members.