I have a couple things to add to this. But I do want to start with "yes, background count will not affect a power like Freefall."
Any power that does not call for or modify a test in any way does not get affected by Background Counts. Missions has narrowed that classification further and apparently only has background apply to Skill tests, but that's a different matter.
Freefall does none of those things, it gives a unique ability, but doesn't affect any skills or call for tests. However, I would warn that player that some GMs may have background affect some jumping tests on an adept with the freefall power (though I would be hesitant to do so myself). And I could also see it applying to attacks that were made as a result of using the power (second to last sentence).
Notably, background does apply to any skill test that has been affected in any way by magic. That includes combat damage from killing hands or critical strike. It doesn't have to only include the numbers on the skill test itself.