Programs: AA LT Gold, 1.7 MM flying my way to LT PLAT
Bag stealers in my area take the whole bag and don't care if they knock you down doing it. A lot of women get badly hurt trying to hang on to their bags. I agree about not carrying anything of value in a bag when traveling, but I do the same at home and at work.
Besides the somewhat nihilistic advice not to carry a bag or not to carry anything valuable, the best way to safely carry a bag is to have a double attachment. There are messenger bags that have a shoulder strap that is worn across the torso (instead of only over one shoulder). In addition, some of the these bags have a belt strap that goes around the belly. It's like a harness.
A thief would literally have to knock you down and take it off from you. A grab and run is simply not possible. Naturally, a backpack with hip belt and sternum strap would be even safer.
Basically, the best way, combining different safety approaches would be to take a Pacsafe bag and add a second belt, which is not difficult.
You will never be totally safe but unless they knock you down or hold you at gunpoint they won't get that bag or its contents.
Do you leave your house unlocked? Do you leave your car keys in the ignition? Though you know you can still be burglarized or your car stolen, you probably lock up and keep your keys in your pocket. While I can answer yes to both questions in my rural town, when I travel I take reasonable precautions. A thief dedicated to robbing you at home or while traveling is going to get the job done. The more savvy you look, the more prepared you are, the less you are going to attract the street thieves who depend on stealth, speed, and an easy mark. I have a PacSafe fanny pack that locks on, and worn off to the side makes a nice armrest. While I actually use it more in the wilderness to keep my survival gear on my person in case of seperation from my mighty steed, I take it when I travel to places I wouldn't want to carry a bag. Nothing is 100% able to keep you safe, but, hey, it's a nice enough looking bag and suitable for male or female.
I agree with you that nothing is full proof, but I've seen security mechanisms that are so compromised that they don't stop thieves at all any more. For example, a steering lock column might have been a minor deterrence when thieves were actually crossing wires to start a car. Once they moved to attacking the ignition cylinder or the column, a steering lock column's protection became completely ineffectual. A hologram deterred credit card counterfeiters when they first came up, but now you can't buy a counterfeit credit card blank which doesn't have the hologram in place and looking perfect.
You cut through ninety percent of the strap when the person is standing still and then take off running and the strap breaks. If the thief moved from a sharp blade to a cutter as his default tool, the Pacsafe would be useless. If the side panel isn't protected and that is where people normally cut, the bag isn't protective.
A fanny pack is safer than a shoulder bag, but it's still an attractive and easy target for pick pockets in crowds, like in museum lines and on buses, and most of them can be cut through. I buy travel clothes with lots of exterior and interior pockets -- I like the ones made Tilley, which have the added advantage that many of the external pockets are velcro-sealed, meaning they make a noticeable noise if someone opens them.
I also sometimes use pouches that have a big loop, big as the pouch itself, you can put your belt through. These of course can be cut through, but they probably won't be cut off, since the large size of the loop means it would actually be harder to cut it off your belt than to cut through it. You can wear these in front, where you can casually keep your hand over it when you're in a crowded place.
If you really need to carry something in a bag, and you're not in a place you know is safe, it's best to carry your stuff in a rather used-looking plastic or even paper shopping bag from a medium-priced (not luxury) local store. This suggests that you're a local, and that what you have in the bag is more likely to be a salami sandwich and a bottle of mineral water than a passport and camera.
The 'fanny' pack I have (which is never behind me) is slash proof, excepting maybe the back which is against my body. I could loop the strap through my belt loops, but I just wear snugly. A thief could cut through it with wire cutters if I were cooperative enough, I suppose, but all accessable surfaces are slashproof.
Good idea about the local looking shop bag!