oncebitten: There is a vast difference between the two.
I don't see it. The JW explanation is that JWs can ask forgiveness from Jehovah by using Jesus as an intermediary. He offers his blood to pay that price. Thus, his sacrifice covers the sins of humanity. Adam's actions locked the door to salvation, and Jesus's actions unlocked it. If the objection is that his sacrifice is not automatic (that is, that one must repent before it can be appliced), I don't see an issue. It's the opportunity that matters.
Don't get me wrong, I think the whole concept is overwrought. Nothing stops god from simply forgiving us without requiring that blood be spilled. But I don't see a difference between "Jesus dying for Adam's sin" and "Jesus dying for our sins," because the mechanics lead to the same end result. If anything, the JW version is a poorly-worded explanation that was probably borne out of their need to be contrary about even minor details. The Rutherford Effect, if you will.