As others have mentioned, renting is different from simply using a device that belongs to someone else. If nothing else, there are legally binding contracts that are signed, and I doubt those contracts include a provision about being able to use the computer to spy on you. Besides, what happens in a rent-to-own situation as was the case here? These people paid-off the computer and owned it, but Aaron's still had the capability to spy on them, and used that capability.
A company that gives computers to a employee usually does so with the express purpose that the computer is to be used to perform the duties of employment only. Therefore, the company may block ports, install monitoring software, etc.. all to ensure that the computer is being used under the terms agreed to by the employee.
However, all Aaron's has to do is say they were monitoring activity to ensure that the renter's weren't using it to download kiddie porn, and the courts will probably side with Aaron's. I remember stories about rental agencies monitoring the movements of rental cars, not that they thought these cars had been stolen, but simply so that they could fine the renters for violating speed limits (the contract states the renter will abide by certain rules). Here's a link:
http://news.cnet.com/2100-1040-268747.html It's about 10-years old. I find it sad that the article talks about the need to create new privacy laws before the incoming wave of cell phones and GPS devices hits, and that those laws never came about (if the recent complaints against Apple, Microsoft, and Google tracking cell phones are any indication).