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A diminished 7th chord is built with two tri-tones, which means it could represent four dominant chords:

Let's try to fit these chords to the key of B-flat, which is the key of the moment of this song, Someday My Prince Will Come. This is not a theoretical analysis since we are not considering what chord might follow.

• A7 = possible V7 of iii-: the scale would be Altered Mixo
  
• But on stage, we often like to play A7(b9,b13) instead, to make it more interesting
  
• Eb7 = possible SubV of iii-: the scale would be Lydian b7/Mixo #11
  
• C7 = possible V of V: the scale would be Straight Mixo
  
• Gb7 = possible SubV of V: the scale would be Lydian b7/Mixo #11
  

Which one of them has all the chord tones of C#dim7? The answer is A7(b9,b13).

Let's compare the scale:

If you add C natural, which is a #9th of A7, and often added when the b9th is used, the resulting scale is identical. Coming up with a cool phrase on A7(b9,b13) is a lot easier than sight reading C#dim7 and trying to figure out the non chord tones according to the key of the moment.