Squire James
Explorer
Double Swords. Swordmages. It's not only two weapons, it's two different implement types.
I do not agree with your premise that the mere existence of Swordmages and double weapons proves the existence of "double implements". In this instance, I think you still have a swordmage with a double weapon that can be used as a SINGLE implement. Of course, this could be defined as a "grey area" since I don't think I see a section on "Swordmages and Double Weapons" anywhere in a rulebook.
At any rate, regardless of explanations, I choose to use Occam's Razor on the whole matter and simply rule that Dual Implement Spellcaster requires the use of two unconnected objects. Of course, this decision is easier since I allow neither swordmages nor double weapons in my campaign (for flavor reasons, not balance reasons).