Jigsaw: Live or die. Make your choice. Let the game begin.
Jigsaw: Congratulations. You are still alive. Most people are so ungrateful to be alive. But not you. Not anymore.
Adam: My name is very fucking confused.
Adam: I don't give a crap if you covered yourself and had a 15 hooker gang bang.
Chosen answer: Yes. You pretty much guessed correctly. We can assume that Jigsaw told Zep to tell Ali to tell Dr Gordon, "do not believe Adam's lies..." Don't forget that Jigsaw spends hours planning his tests so it would be safe to say that he had planned it all in the beginning.