Diminshed Whole Tone?

I have a problem and I need your help. This is a jazz theory problem that involves a chord scale relationship. I have a few Aebersold play-along books and they all have the following chord at some point:




Now, I have no problem with understanding the chord itself, that's the easy part. It's the next part that is confusing me. Aebersold goes on to say that the scale that is best used for this chord is the diminished whole tone scale. This scale not only has a #9, it also has a b9, #4, and #5, so the scale looks like this:



How did he come up with that? No explanation is given; I have found no theoretical reason as to why the scale has the additional altered tones. Could someone please help me understand this? If you've never used the scale in context, it's a great scale. There's a lot of tension and resolution possibilities, I just want to know why and how this scale came to be. Who decided and for what reason that the scale for a c7+9 chord has a b9, #4, and #5? Help me understand this.