Connection between Late Show with David Letterman and The National Council of Churches?

This morning while reading about the release of “Voices of Christmas from the National Council of Churches" I noticed a reference to it being played Christmas eve during the normal 11:35pm late show time slot on CBS. I don't think it's just by chance that this special is showing on CBS and during the letterman time slot. For many years now The Late Show has been creating these joke video bits and at the end the announcer will come on and say "This message has been brought to you by The National Council of Churches. Back to you, Dave." Here is my wild guess. I think David Letterman's production company Worldwide Pants Incorporated does some work for The National Council of Churches and possibly even produced this Christmas Special. They made the deal and offered up the late show time slot for some discount. If someone knows the real connection please comment below.