Glenn Miller's "Over the Rainbow"

When I listened to a Glenn Miller compilation album back in March, I noticed something interesting about his version of "Over the Rainbow."  Two days ago, I listened to Judy Garland's version from The Wizard of Oz and Glenn Miller's version again to compare them.  Lyrically, the verses in both are the same, but then things start to diverge.  In Garland's version, there are short segments following the verses:

Somewhere over the rainbow, bluebirds fly
Birds fly over the rainbow, why then, oh, why can’t I? 

If happy little bluebirds fly
Beyond the rainbow, why, oh, why can’t I?

Miller's version has only one of these, but the lyrics of the second half of the first line are different:

Somewhere over the rainbow, skies are blue
Birds fly over the rainbow, why then, oh, why, can’t I?

Instead of "bluebirds fly," Miller's version has "skies are blue."  "Somewhere over the rainbow, skies are blue" is a line in the song (the third line of the first verse), so it's not a drastic divergence, but - significantly - replacing "bluebirds fly" with "skies are blue" disrupts the rhyme scheme.  "Fly" and "I" rhyme, but "blue" and "I" don't.

The half-substitution of that line might just be a mistake, but the strain it causes by not rhyming still relates to the lyrics nicely.  There's an incompleteness because there isn't a rhyme, and that same lack is in the lamentation "why then, oh, why, can't I?"