It may not be entirely consistent with the show, though, since if airbenders could pop up from anywhere they couldn't have been nearly so certain they were ending the Avatar cycle by killing all the monks.
That kills the theory, if airbenders could come from any nation during Sozin's times (which couldn't be a secret) there would have been no point in attacking them in the first place unless the goal was to kill the avatar specifically and that would have only led to a watertribe avatar who was a few years younger.
I took some time to rewatch the Korra finale and think about it and the things people wrote in this thread in its defence. My opinion hasn't changed much, I still think the final scene was awul and nothing but crappy writing.
I can deal with Amon waterbending to save his life, but I still think the way he did it was out of character for him. Using waterbending to get to the surface? Sure, that makes sense, but emerging from the water and floating in midair on top of a giant water column for such a long time? That was too much.