I don't know what you think I believe about the bottom line.
Oops, I wasn't clear. This part:
I don't buy the idea that Walmart's margins are so thin that the store has to prosecute petty theft...
I don't either. It's a difference between micro and macro price margins, but the dichotomy is false.
Anyway, I would chalk most of the clientele difference to Walmart's reputation. It may not actually be cheaper (though it is, often, cheaper than everything except Costco), and most of the calls may not actually come at 2am, but nonetheless its hours and perceived prices contribute to it seeming like the 'trashier' big box store. Can you imagine someone mixing meth in the bathroom of a Target?
Target is also committed to customer service in a way that Walmart isn't, of course.
It may make sense to Walmart's culture to operate this way, but I'm not convinced that it makes financial sense. For all the hours that it takes a police officer to respond to a theft, it also takes a Walmart employee's time to deal with the incident. That employee gets paid for that time. If the police hours are that high, then the Walmart employee hours are high as well. If Walmart used that money that they would have used to pay those employees, they could pay a loss prevention consultant team to find ways to reduce the theft or pay a security company to patrol.
Maybe. But the people who run Walmart right now are some of the most successful businessmen and women who ever lived. And as far as loss prevention goes, it's just as easy to shoplift from Target as it is from Walmart.