Bush speech "outtake?"

Factual Questions
1

Last night I watched both Letterman and Leno, who showed a clip from the President’s recent speech. He said a couple of sentences then suddenly stopped and looked around as if a bit confused.

I didn’t see the actual speech, but don’t think this clip was actually broadcast (was it?). I suspect it was a practice run through, that made it to tape, and eventually wound up being broadcast or somehow passed into someone’s hands who made it public.

Is this what really happened? or how did this clip come about?

2

CNN cut too soon to the Oval Office, and caught Bush in mid-rehearsal.

This link has the video - note: it starts playing video and sound automatically.

3

That video went out live on CNN.
Here it is with a bit of explanation as to what happened. It seems that NBC cued the president early, CNN broadcast it, then the president had to start over at the correct time for the other networks.