I understand your argument but unfortunately it wont fly in the media. The left wing will simply ignore what you say and keep repeating that Cruz, unlike Obummer, was foreign born. The target of this will not be to convince us who are informed but to simplify the issue into a talking point for the unwashed. (Alinsky)
Which didn't seem to be a problem for McCain, which can also be pointed out. But the idea is not to defend Cruz, but that both Cruz and Obama are ineligible. The reasons that make Cruz ineligible are the same for Obama.