That's completely stupid.
Firstly, Otaku doesn't necesarily have anything to do with anime or manga. You could be an Otaku obsessed with trains or the military. Essentially it is the Japanese equivalent of a super nerd.
Secondly, it's a japanese word used to describe super nerds. Which means it can be applied to gaijin too. That is like saying that western toilets are not "toire" because only Japanese toilets can be called by the Japanese name for toilet. (Yeah, a mouthful I know, but you get the point). It's isn't only used on Japanese people obsessed with anime. That's like telling a Japanese person that they can not be called a nerd, because it's an English word. They will only ever be an otaku. It's the same thing in a different language!
It's just like anime. It isn't even a Japanese word. It's katakana. It's borrowed. A Japanese person calls western animation anime as well. It's there word for animation. We just twisted it so that we believe only Japanese animation can be called anime. That's why Japanimation is a much more correct word.