As the rule currently states, restricted crime zones only apply to muggings and kidnappings with intent to mug. To quote the rule: "Other crimes in these areas, particularly crime that grabs attention such as shooting, are held to a higher standard." - This doesn't mean that other crimes require approval or supervision, and do not cover that report's specific case, it being a vehicle being lockpicked very early in the morning.
Crimes that don't involve the two above mentioned are not affected at all. Carjacking isn't a mugging or asportation! But other rules come into play, like doing so with no fear of being caught because of a low player-base and the lower likelyhood of someone actually stumbling upon such scenario.