Somehow, I doubt that this is what was recorded. "Allah akbar" seems much more likely, and should have been translated as "Allah is great".
Allah is not God.
It sounds like you're correct. Here's an excerpt from the Newsweek article
In their instructions the hijackers were told: Shout Allahu akbar, because this strikes fear in the hearts of the unbelievers.But it also says later on in the article:
The hijackers cry out, God is great!