I think this argument is rubbish. Claim 2 seems like obvious bullshit, unless "identical" is given some weird technical meaning that makes claim 1 bullshit instead. Further, with the sense of "possible" that's relevant here it's very far from clear that anyone's shown that zombies are possible. (The SEP page treats this point quite well.)
I have used the following parallels before: I can imagine electric current flowing without any charged particles being present, "therefore" electric current is not the same thing as the movement of charged particles; I can imagine my computer continuing to do what it does without its circuitry and what happens therein, "therefore" the processing my computer does is not a mere activity of its circuitry. What twaddle. (See http://www.mccaughan.org.uk/g/log/2007/inconceivable.html for a longer rant on the subject, complete with a couple of quotations to show that some philosophers really do think such silly things in the case of consciousness.)