Travel wallets are not a fool proof means to protect yourself from theft but they are better than walking around with a wallet in stuffed into your back pocket. Travel wallets that you can wear around your waist or hips under your clothing provide good protection for valuable documents when on the street or on public transport. They are completely useless if you wear them outside your clothing. You might as well have $100 bills taped to your shirt. Cheap travel wallets are made from cheap materials that sweat against your skin. Brazil is a hot and humid country. It is worth spending a few extra dollars, buy quality, and not look like you've wet your pants on a hot day in Rio.
Worst Case Scenario
You are mugged at gun/knife point by a gang of youths who demand your wallet and all your valuables. It's a pretty simple choice. Just give it to them. If you are not shot, stabbed or heavily beaten what have you lost? A camera, watch and a few photos? Travel insurance will cover all of it but the photos.
Lets look at the situation from the thief's point of view. Here is a rich tourist from a first world country with so much money they can not only take an extended holiday but fly overseas for it. Robbing you presents a risk for them as well as you so they want to do the job as quickly as possible with the minimum of fuss. Shooting you attracts attention and dead tourists attract unwanted attention from the police. This is bad for future business. They need tourists to keep coming back in order to run a sustainable business. Therefore the gun/knife is a very effective motivation tool but they really don't want to use it unless you force them to. Do something stupid or heroic and they might have to.