Although I am getting slightly odd results from the National Rail Enquiries journey planner (valid on via Coventry & Rugby services but not valid on via Coventry & Bedworth), the East Coast website is giving me via Coventry & Rugby, and via Coventry & Bedworth, itineraries for this fare.
Having looked at the routeing guide on the ATOC website, the map combinations for Stafford-Nuneaton are: TL; and CC+WM. These do not offer a via Coventry route.
There seem not to be any through trains from Stafford to Nuneaton via Coventry.
And while Stafford-Nuneaton is only 36.5 miles, Stafford-Birmingham-Coventry-Nuneaton is 58 miles, so via Coventry is not going to be permitted on the ground of being the shortest route.
However, the trainscanbecheaper website suggests that in the electronic routeing guide, but not the public version, map WM does allow Birmingham-Coventry-Rugby-Nuneaton (but not Birmingham-Coventry-Bedworth-Nuneaton). This, I think, explains the result that I was getting from the NRE journey planner.