What camera(s)/gear are you carrying? It makes a lot of difference in bag selection and how you are perceived. The smaller camera in a fanny/bum pack on the waist is pretty low-profile. A large bag, well, it certainly has a lot more bang for the buck for a potential theft, IMO, which could include electronics like iPads, phones, iPods, wallets, etc.
First rule of being safe is your location choice. Second rule is whether or not you appear vulnerable. I rather like the Smith and Wesson T-shirts myself.😛
Personally, there are things you can do without carrying a diaper bag. If I could afford insurance, I would certainly have it. If I could afford the risk of going to rather risky areas, I would still avoid it, just not my interest. But a man has to have a certain minimum standard of style and IMO a diaper bag ain't it!🙂