In my opinion, the city is as safe as you make it. Common sense goes a long way. That said, when I interviewed for medical school here, they told us that only 5 med students had their car stolen that year (which was apparently down from previous years). I know multiple students who have had their homes broken into. A guy who robbed the hospital cafateria was shot to death by police outside our education building a few months back. You have to learn to let these things roll off your back.
The simple fact of the matter is that the city has a HUGE population of people living below the poverty line. The city has its fair share of crack addicts, gang bangers, and 17 year-old girls on their 5th pregnancy. So when people say "the worst part of the program is its city", you have to realize you deal with these types of people on a daily basis. It wears on you after a while and you begin to lose faith in patients. That said, Memphis can be a very fun city if you use common sense when choosing where to live, do things to minimize your risk, and try to realize not everyone that walks into the hospital is addicted to drugs. The Med is where you'll do a lot of your training and the area draws in a less than reputable crowd at times. But there are also multiple training locations out in the suburbs where you won't run into these problems.
Campbell's is such an incredible group of individuals that I would live in any city to obtain the training that these guys get. You also have to realize that this kind of patient population is often so grateful to get any help at all. Final word, the city definitely has some problems but the advantages of this program far outweigh them.