Pay attention to the number of strange coincidences. This business of "mathematically impossible" has a double meaning, I think. There are Q-proofs, but there are also Divine proofs. Which is good for the mission, because I don't think a few good intelligence people could clean up this mess without help from Above.
As an avid sci-fi reader, I found myself constantly suspending disbelief about advanced alien civilizations with seemingly endless "powers". So I asked myself why I wasn't suspending disbelief about God. So I did.
God be with you.