The Legend of Korra

It was never Avatar exclusive. The Lion Turtle said it himself: Before there were benders of the elements, they bended the energy around themselves. It just so happens that Amon knows how to do it. Though I guess that means he has a ridiculously incorruptible spirit to take away people's bending, but incorruptible in the bad way :C But since he can take away Bending, it means that he himself is a bender, so ironically, the anti-bender uprising he is leading is being led by a bender. I find it weird that people did yell at him before- they know how Aang defeated Ozai and that it is called energy bending (and it seems noted in history), why aren't they casting Amon out for being a bender?

I understand that the Lion-Turtle said it wasn't, however how Tenzin responded to it made it sound like it was an Avatar exclusive ability. He said something akin to "Only the Avatar has possessed that ability!"

Honestly though we don't exactly know how knowledgeable the people are about how Aang actually defeated Ozai. For all we know, all they know is that he beat him, and that's it. Considering it stopped a 100 year war, mass murder, and the Fire Nation's takeover of the entire world, that's all that's really needed for him to become the hero he's known as in Korra's time. The Energybending aspect of it might have been lost in the 80 years, thrown away as a myth, or simply never spread as the true way Aang defeated Ozai.