Bird Names

Why is a South American bird called a bamboo tyrant, am I wrong in thinking that bamboo was only native to Asia?

Edit: Yes, yes I am. Apparently native to the whole southern hemisphere (Except Aus/NZ because fuck us right Wallace Line?). And so much more than just the cliche bamboo I’m thinking of.

Edit2: https://en.wikipedia.org/wiki/Pooideae what a shitty name.