Found it, finally.
Yes, in a situation like a mugging defending yourself with a firearm can escalate things further than they would have it you just hand them your wallet. That is why you must use your best judgment and keep a cool head. If the criminal looks benign then throw him your cash and tell him to screw while you back away toward other people. That is easier than getting into an altercation and having to get an attorney, etc... But if he comes at you after you toss him your cash you have a big decision to make. People who rob you automatically are not the most level headed, and I would rather be the guy with the bigger stick, so to speak.
Another solution is to only carry plastic. I don't carry more than $20 in cash unless I plan on spending it that day. But usually I use plastic and carry cash for highway robbery, er, I mean, tolls. Take away the cash element and muggings will go down, but home invasions may go up Backing down from criminal elements should be avoided by any society looking to actually fix a problem.
How often do they just want your cash? I've never been robbed or burglarized, so can't speak from personal experience. I'd think they would want the whole wallet/purse, since there would be a better chance of getting all your money, not just the $20 bill you offer. It's not like they are panhandling. With your wallet, they know where you live, and can find you later if needed before any trial. The information most people carry, is good enough to steal an identity. Besides the cash, you get to waste time and more money replacing your identification and plastic, and a piece of animal hide.