That's the problem. You're oversimplifying. The human genome isn't that simple, and in this case your simplification omits important details.
You're correct in saying that the odds of two parent organisms, each carriers of a recessive gene, giving birth to two offspring that both have the recessive reinforced is 1/42. But that's not 1/8, it's 1/16 :)
But again, human genetics isn't that simple. Another way of looking at it, though still oversimplified, is this: there are two gene locations, one of which specifies either fair hair (F) or dark hair (D), and the other of which specifies either red hair (R) or non-red hair (N). Fair hair is recessive while red hair is dominant. A child who has genes for both fair and red hair will be a redhead.
Suppose John Thune is FD RR, while Kimberley Thune is FF NN. Their chances of having a single redheaded offspring are 50%, and two redheaded offspring are 25%. This, again, is an oversimplification of the actual genome, but is closer to reality than the 6.7% you came up with.
I know it isn't that simple. I am trying to remember genetics as it was taught to me in high school 35 years ago in biology class; it's not my professional field now. I do have a basic understanding of this before they put rubbers on cucumbers recently, do you agree?
We have the correct math together. Shall we say that each child has the same chances at these genes as the one before it? I am looking at probability mathematically as you are looking at it biologically. We agree on the solution and disagree on the approach. Because we are in different fields of expertise.
Let's talk some more about this tomorrow or so because I must sleep. And I want to sleep as late as I am humanly able to tomorrow.