Alright. Using Monday the 6th of July, National Rail Enquiries does recommend the following itinerary for Sowerby Bridge to Birmingham International:
6.04 Sowerby Bridge > 7.01 Salford Crescent (Northern)
7.06 Salford Crescent > 7.15 Manchester Picc (Northern)
7.27 Manchester Picc > 9.13 Birmingham International (XC)
It took me a while to notice this, as it involves doubling back between two map points, so it looks wrong, but travel via Salford Crescent is allowed under the within three miles of the shortest route rule.
The OP's route is entirely permitted.
I am pleased to hear my logic was faulty, and that, indeed, the OP had a valid ticket from Sowerby Bridge to Manchester Piccadilly for the route taken, and wish him all the best.
My apologies to the OP if my post caused added stress. Should I have not posted? I believe the outcome gives him a little more ammunition in fighting the injustice he has suffered. The routing rules, although arcane are the railway's after all.
Just for completion the excellent railmiles website gives rail distances in miles and chains (80 chains=1 mile) as:
2m 34ch Manchester Victoria - Manchester Piccadilly (via the new Ordsall chord) is the shortest route
1m 59ch Manchester Victoria - Salford Crescent
2m 29ch Salford Crescent - Manchester Piccadilly
So by my calculation it's 4m 8ch from Man Vic-Man Picc via Salford Crescent (1m 59ch + 2m 29ch)
and the difference between the two routes is 1m 54ch (4m 8ch - 2m 34ch), so is indeed well within 3m of the shortest route.