So based on that, I'm assuming that spirit-bending is a separate, fifth form of bending.
You don't have to assume, we know it's seperate. The lion turtle said (I'm paraphrasing) "Before the avatar we did not bent the elements, we bent the spirit"
For some reason spritbenders were not made part of the avatar cycle and the ability was lost over time, there could still be spritbenders but because bending is now all about tangible elements they never realized their abilities (until a certain spirit who's not exactly a fan of the avatar found Amon and flat out told him).
The avatar can spiritbend because being able to bend all elements (even the one not part of the cycle) defines him/her.
Or maybe spiritbending was and still is the base of all bending and air, water, earth and firebending are just specialized forms of it. Every bender is a spiritbender just like every metalbender is an earthbender, spiritbending was just forgotten over time.
This also fits my other theory, that there is no genetic element to bending at all, every bender has the potential to bend every element at birth, the reason the water tribes only produce waterbenders is because their entire culture is build around water. If two waterbenders lived in Republic City their child could turn out to be a firebender. In an integrated society that doesn't groom the bender to be in tune with one specific element from birth the bending could manifest itself to suit the benders personality.
Edit: replace spiritbending with energybending if you like, who cares, doesn't change the theory.