Brazil, similar to many countries around the world, makes revenue from US tourist. They do not discourage tourism. If verifiable negativity towards US citizens is reported on newsnetworks, it will discourage travel.
They understand this concept. It is no different than Los Angeles in the respect that you must exercise common sense. Read up on Lonely Planet among others and learn the ropes. Most of all, use your instincts when you are there. If you think withdrawing cash from a certain ATM looks unsafe, go with your gut
Don't be the typical "American." Our country tends to hold little regard for other cultures and usually is guilty of not understanding them.