I've never seen street-crime cited as reasons not to visit any of those countries; and nobody with an opinion I respect has advised in any way against travel to Syria or Jordan.

The situation in Rio has improved significantly over the years I have been visiting. Of course the authorities care: the tourism industry is important to the state and the city, as is the security of residents. But Rio's extremes of wealth/consumption and poverty/hopelessness in very close proximity, coupled with easy pickings from less-than-careful tourists, makes an explosive mix. It's difficult to fully control in a way acceptable to all parties, and tackling the root causes will take many years. In the meantime, Rio is not a place to avoid, just one where you should exercise caution.