Basic Firebender: Manipulates flames.
Intermediate Firebender: Create and manipulate flames from intense heat source (ie. burning coal,lava, sozin's comet).
Master Firebender: Manipulates the intense heat source itself. (ie. lava, burning coal).
Had similar thoughts... here's my reasoning on the subject:
Example 1: "The Drill" - Katara and Toph bend the slag.
Here we have both katara and Toph being able to manipulate the slag because it contains their element. Both are bending it together, but do not need the other type of bending to do it alone.
Example 2: Bloodbending
Waterbenders can bend creatures + people because they contain water. There's a multitude of other materials in there, but only waterbending is needed to bend them.
Example 3: "The Avatar and the Firelord" - Sozin removes the heat from the lava, freezing it.
This, I believe, is the major clue as to how lavabending works. Sozin is clearly not bending fire, but the heat. He's transferring it to the air, then through his body (like redirecting lightning) then out into the air again. I believe this means that firebending is not literally firebending, but heatbending. Fire in our world is simply the glow of the heated gases and air rising from whatever it is that is burning. In other words, when a firebender throws fire, the fire is simply a result of the heat that he is projecting forward.
What does all this mean? Since lava contains massive amounts of heat, firebenders can control it. Obviously, earthbenders can control it as well, but skilled firebenders (Avatar state) can manipulate it.