This shouldn't be mixed up with the other common case which is often discussed, 'American' as the demonym for people and things from the USA. That isn't quite as bad (though it still annoys other people from elsewhere in the Americas) because it's using the name of the superset - Americans, from the USA, are also Americans, from the continent. Whereas, when "America" (the USA) does something, it doesn't necessarily mean all of America does it. The USA is a subset of America, not a superset or the only entry.
Language isn't always logical, but if you won't draw the line at something so clearly backwards as using the whole continent's name for the actions of one country, you can only expect it will start an argument every time.
So, yeah... you can say brazil borrowed that word from the greek language via latin, and the greeks themselves borrowed it from an extinct language...
Am·a·zon /ˈaməˌzän,ˈaməzən/ Learn to pronounce Origin late Middle English: via Latin from Greek Amazōn, explained by the Greeks as ‘without a breast’ (as if from a- ‘without’ + mazos ‘breast’), referring to the fable that the Amazons cut off the right breast so as not to interfere with the use of a bow, but probably a folk etymology of an unknown foreign word.