There is no convincing evidence that arrest rates "severely" overestimate offense rates; if anything it is just as likely arrest rates underestimate offense rates.
While what you say specifically is true, using arrest rates to determine criminal activity by race (and the subsequent conviction rate, etc.) has been shown to have strong relationship to race; at least in the United States. There are entire books on the subject. You can't tie racial arrest rates to the underlying crime rate, as POC get arrested far more often for the same crimes.
I'm not sure I understand that correctly. Are you saying that POC are acquitted or have charges dropped far more often for the same crimes (i.e. have a far lower conviction rate)?
POC are more likely to be pulled over, then when pulled over more likely to ask to be searched, then when searched more likely to be arrested when situations are similar to non-POC folks.
It doesn't really stop there either, they are more likely to be convicted of the same crimes and then get longer sentences. They are less likely to be offered probation.
This eliminates huge percentages of men permanently from POC communities. It is possible that this process can be blamed for the social issues present in the inner city.
"The New Jim Crow" covers a lot more in a lot more detail. I would strongly recommend the read.
In general, POC are more likely to be arrested for committing a crime.
The parent's point isn't about whether they are acquitted, it's that if you were to commit a crime as a POC, you are more likely to be arrested than if you had committed that same crime as a non-POC. In both scenarios you committed a crime, but in one of them the system never has a record of it. This is why arrest rates and crime rates are different: if a POC is more likely to get arrested for committing a crime, the arrest rates by race (POCs get arrested more) will not reflect the crime rates by race (differences are generally smaller).
Communities of color are over-policed. There's a huge racial divide in income, and crimes that tend to be committed by the poor (like shoplifting, loitering, and fare-evasion) are far more likely to be prosecuted than crimes committed by the wealthy (smoking some weed in your suburban living room, fudging your taxes a bit). The end result is that people of color are more likely to have an arrest record, even if they're just as likely to commit a crime as a white person.
For an example of this backed up by data, the NYPD stop-and-frisk program has always overwhelmingly focused on black and Latino people (almost 90% of all people stopped in some years), even though they make up only 15% of the population of some of the precincts involved AND white people were more individually likely to actually have an illegal weapon (the supposed reason for the stop-and-frisk program to exist).
Just to add a bit, you can look at the justice system as a binary classifier if you squint hard enough. So it has both false positives and false negatives, both of which are difficult to actually measure.
On the one hand, you have poc arrested and convicted of crimes that wouldn't be charged in other parts of town (arguably false negatives, amongst the non poc). On the other, prosecutors use the plea bargain system to get people to plea out for smaller charges instead of risking decades of their lives at trial; this is an excellent way to produce false positives.
