FWIW a couple of years ago I was involved in a court case where there was a subpoena sent to Luminati to figure out whether or not a specific request had originated from their network, lawyers Luminati replied that they do not keep any logs whatsoever as they aren't required to do so under Israeli law.

Hard to imagine any serious anti-abuse efforts by Luminati if they don't monitor what their users are doing, but this is probably a deliberate effort to avoid potential liability arising from knowing what their users are doing.