See now, in that series the reasoning explained for the red/blue shift is something moving toward or away from us. Anything moving toward us is slightly blue, and anything moving away from us is slightly red. This is in the scene with the car on the road btw, in case you wanted to look it up.
And since everything in the sky is moving away from us near the speed of light, we see everything as slightly red. Not very red, only slightly red. One would assume that the speed at which something is moving toward or away from you is the key to a red/blue shift in color.
Unless the discovery channel, in cooperation with Mr. Hawking, got it wrong of course. Lets face it, TV channels aren't exactly known for their fact checking. I'd get you a video link, but I'm at work at the moment