A (new enough) tow truck screams "I have an ongoing business relationship with people who have badges, guns and letters of marque that give them permission to ruin and/or end your life at their discretion" which is really why none of the people who would perhaps bother a common thief or stick their nose in anything out of the ordinary will get near a tow truck.

You could roll up to a parking lot with active security and snatch something with a tow truck and they won't bother you most of the time whereas if you rolled up to engage in swapping a battery or some other legitimate repair they'd probably at least come over and ask what you're up to.