Do you see the problem with your statement here. The word crime is a selection bias filter. You automatically assumed that high IQ people committed less crime and immediately discounted they get caught less for crime.

These styles of biases are rife in law enforcement communities. For example the idea that (poor|ignorant|minority) groups do more drugs than the average person. Therefore the police search those groups more and when they find drugs it is a justification for their behavior. Meanwhile studies outside of law enforcement show that illegal drug use across all spectrums of wealth, IQ, and race are similar.

Also, another similar observation is the saying "You're likely to be murdered by someone you know 70% of the time". The problem with that statement is it only take in account solved murders. The other 33% (or way higher in some places) of cases that are unsolved are not counted in that statistic. If we had perfect information on who committed a murder we might say that "50% of the time you are murdered by someone you know". This may have a major influence on how cases are handled. Juries are lead to believe that in the majority of cases it is someone the murderer knew and they become biased against the charge. If it was a 50/50 thing a jury may not be as willing to pin a conviction on circumstantial evidence. That said, it may also be that those 70% of murder cases that convict someone the victim knew are correct and murdering someone you know is a good way to get caught.

tl;dr, be careful using law enforcement statistics. Systemic bias in law enforcement procedure can make them invalid.