Also, the point of the treaty is to ensure the extra-national person gets legal representation etc. Which in a U.S. Capital Murder case, he has gotten in spades.
The lynchpin of the Obama admin and Mexican .gov's arguments is that he did not get embassy counsel, which may have led to him making statements and waiving Miranda rights.
Shrug, my understanding of the case is that he was covered in the girl's blood, so what he said probably didn't make much difference.