In quite a few years I have been robbed twice. A couple of other times people have tried, unsuccessfully, to rob me (throwing mustard trick etc). Of course I am very careful and wary. Many tourists are NOT. I think a lot of American tourists, like quite a few expats, come from suburban middle class USA and have little experience living in cities. The huge BA metropolis is something new to them and they are not always careful. Many backpackers (the backpack alone is an ad that you are a tourist) put their wallets and passports in the back pocket of the backpack and get robbed. Not a very sensible way to travel!
There is no doubt that BA is full of thieves. My impression is that most of it is non-violent stealing but with all the drugs going around there is risk that it could turn violent. Some places (La Boca, San Telmo - especially Plaza Dorrego) are high risk pickpocketing areas. I know lots of people who've had problems there.
I feel safer in New York than I do in BA -- sorry I know some expats will attack me for this. I am speaking of Manhattan, not the Bronx, Brooklyn or marginal areas. Comparing the better parts of BA with the equivalent in New York I feel safer in NY where I have never been robbed either when I lived there or on countless trips over the years. I don't feel nearly as safe in many parts of Europe. It's easy to get robbed in Rome, Paris, etc. There are even thieves prowling European trains at night.
What really disturbs me in BA are all the shops with locked doors. This accelerated during the "crisis". Now it's widespread and it is disturbing to have to ring a bell to be admitted to a shop in Recoleta or other upscale parts of the city. I've never seen this anywhere in the US and can't recall it in Europe. It certainly has to be unsettling to tourists.