Please look at my question this way: It's not your explanation, but my total befuddlement that is the problem. :-)
Well yes it is, but it's a pic of the light emitted from that deep region of space in particular. At least in that case that light has taken a long time to get here. The light may have been emitted at some other frequency and redshifted, but the temperature equilibrium of the universe demands the average maximum appear at the frequencies corresponding to the present temp.