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Is your friend Japanese because I'm pretty sure it doesn't say that in the article.

First off It would make zero sense to use Fly me to the Moon as a theme song.
That's a song that always played during the ending credits of the OVA series and was used in the trailers.
It's sorta used as a backdrop or a precursor ( not sure if I'm using the right words) to the actual theme song which is usually epic in scale such as Cruel Angel's Thesis and Beautiful World.

They would never use that song as a theme to this movie.
Consider how unbelievably lame that would be?

Here is the official press release to put people's minds at ease:

Japan?s MyCom Journal has confirmed that Utada will once again helm the theme song to the upcoming Evangelion film ?Evangelion 2.0 You Can (Not) Advance,? set for release in Japan on June 27th, 2009. The as yet untitled track will be a follow up to Utada?s 2007 Japanese hit ?Beautiful World,? which was the theme song to ?Evangelion 1.0 You Are (Not) Alone.? No release date or other details for the single/song have been announced.

Check the first post of this thread.