The point of wielding a staff one handed is from the errata on the Eberron Player's Guide (as cited by me above): "The staff is a one handed implement ... a quarterstaff is a two-handed weapon".
Ok, I see it now. But that seems almost a bit of a stretch, tho. That section is talking about component traits. It's hard for me to see how that applies broadly to something different.
I hear what you're saying about implement vs. weapon, and I agree with you: there is a separation of weapon powers and implement powers. I think this was done to prevent power abuse (blood claw staffs or something like that). The thing is, I am having a hard time seeing how that applies to this feat, because they feat is just asking "do you have an implement in each hand?" And when a staff with the Staff Fighting feat gains the off-hand property, even if you're saying that the off-hand property only applies to weapon powers, it still means that you are wielding an item with the off-hand property - which means it has two ends, and each one is its own thing. And while technically each "end" is a weapon, you're still not using a "weapon power" from each end - you're using each end as an implement. How is this different from "a swordmage wielding a double sword"?
re: elecgraystone
I agree with your points, but before you get too far in using the character builder as a source, let me explain the bug.
Create a wizard as instructed, and give him a +3 staff and Dual Impl. Spell. and Staff Fighting. Look at an at-will: he gets a +3 off-hand bonus to damage - check. Now remove the Staff Fighting feat. He still gets a +3 bonus to damage. Curiouser and curiouser. But maybe it's because he is using the staff 2-handed? But now, give him a +1 orb (or whatever) in his off-hand. This should change the off-hand damage to +1, right? But it remains +3. You can give him anything in his off-hand and he will stay with the same off-hand damage as the main hand's enhancement bonus - all he needs is the Dual Impl. Spell. feat.
So yeah, it's bugged. And therefore inconclusive.