Another part of the problem is the historical over-policing of minorities (particularly blacks and hispanics) in the US and the lower economic class. It's easy to view them as more likely to be recidivists until you realize that the neighborhoods they're going back to have more than normal police presence and they're more likely to be picked up for "nuisance" crimes like jaywalking, public drunkenness, and loitering. This will skew the numbers substantially in these sorts of models when the police are (largely) not applying the same standards to white people or those from higher economic classes (or whose neighborhoods are less tolerant of such behavior so it's not seen as often to begin with).
> Proxies for race (such as where they live)
a proxy is only a proxy if there is bad intent, otherwise it is just correlation.
> This will skew the numbers substantially
Only if your analysis is as simplistic - otherwise you can afford to look into the reasons the discrepancy exists.
You suggest over-policing, or higher police scrutiny, results in more arrests - why does it not result in fewer "nuisance" crimes?
(A recent example was a system which predicted recidivism rates among ex-cons, which predicted based on its observed data that a particular demographic was much more likely to re-offend. Rather than asking accepting the result and trying to solve the problem, there was an outcry that the program was 'wrong' and must have been fed biased data.)