From what deeps analysis does this certainty come from? Seems like a propaganda point to me. Of course we cannot say what would have happened without the EU or how that would have come to pass, but I think the burden is on your side for showing that Europe could have gone to war without the EU.

If the question 'why peace?' was come at in a different context, in my opinion the EU would simply not rank as a primary cause. It would be something like (in order)

  - Mutually Assured Destruction
  - US/Soviet military dominance
  - German Holocaust Shame after WW2
  - Rising living standards/post war cultural revolution.
  - End of Empire as a plausible goal for a nation

Furthermore, the UK wasn't a member for decades, and I don't think war was viewed as a possibility at the time it did join.