Wil, if you've had your pockets slashed, you're a victim of a violent crime. That's assault at the very least, more likely attempted robbery, and robbery if you had something stolen.
I can't address your experience though, I can only give you mine. I'm a retired cop with 30+ years street experience. I worked in a major SoCal city for 11 years, and three other more rural departments before I retired. I've been a violent crime victim so many times while I was working that I've lost count over the years. I've only been a victim off-duty once that I can remember, and that was at O'Hare where I turned to pick my bags up off the carousel to find my laptop bag had been stolen from the floor beside me. I was exhausted and had lost my situational awareness that afternoon.
I've traveled to and stayed in many of the major cities in the U.S. (Detroit and New York City being major exceptions) and many major cities outside the U.S. over the years. I've walked, used public transportation, and toured on bikes. When I worked in SoCal I took the trains daily. That's not to say I haven't been in the presence of street crooks... as I have on many occasions while travelling, and I've seen other crimes committed, and been able to intervene in a couple of others. I've walked around some less-than-welcoming (e.g. the Tenderloin in SF etc.) areas with a camera and bag but other than having my carry-on stolen at O'Hare, I've never had encounters such as you describe. That is good because I've discovered over the years that I make an angry and vengeful potential victim, which really isn't a very good thing for a crook, should I catch them trying to victimize me. That will probably change as I continue to age, but for the time being, that's where I am.
So, Wil, I certainly won't discount your experience, but to suggest that I don't have the experience to back up my position or that "I don't know what I'm talking about" is, perhaps, premature.
There is, of course, no magic cloak that protects from criminals, you but you can do much yourself to ensure your own safety. As advice to any of our members here, I would reiterate my suggestion that situational awareness, projecting confidence, and having the ability to be comfortable in your surroundings is still the best deterrent to being made a victim and will do much more for you than your choice of bag.