Doubling back isn't inherently banned; it is permitted in quite a lot of cases:
- As part of the shortest practicable route, e.g. Burton-on-Trent to Uttoxeter via Derby which involves doubling back between Peartree and Derby (since trains from Burton don't stop at Peartree)
- If you are otherwise travelling on the shortest route and the double-back is less than 1.5 miles in each direction, as the route would then still be within 3 miles of the shortest route
- If the stations you are doubling back between are members of the same Routeing Point Group. This is only intended to be permitted for 'interchange' purposes (e.g. doubling back between Deansgate and Manchester Oxford Road because not all trains call at Deansgate) but there is nothing in journey planners which tells people of this restriction, so it's unlikely to be contractually effective.
- If there's an easement which permits it
- If it's done whilst travelling on a direct train from your origin to your destination
- If you're travelling to & from a "via" point specified on your ticket, or London in the case of a journey where one of the mapped route options in the Yellow Pages of the Routeing Guide is shown as "LONDON"
- If you're travelling to & from a common Routeing Point, for local journeys where the stations have the same Routeing Point(s). In fact Stratford-upon-Avon to Solihull via Birmingham is an example which is given in the Routeing Guide instructions (although it's no longer valid since the creation of Tyseley as a Routeing Point).
In this particular instance, doubling back via Warwick is permitted under point number 3 above, since Hatton, Warwick Parkway and Warwick stations make up the Warwick Routeing Point Group.
Obviously it's not a route that makes much sense when direct trains to Stratford-upon-Avon are running. But if they aren't running for whatever reason (e.g. disruption or engineering works) it's a perfectly reasonably route, since most Chiltern services from Moor Street towards Leamington don't stop at Hatton, and most Leamington to Stratford services don't stop at Warwick Parkway.
The Routeing Guide isn't just there to allow routes that make sense under normal circumstances - it is also intended to allow alternative routes that are reasonable. In fact it was intended to encapsulate the routes that would have been deemed to fall within the definition of "any reasonable route" at privatisation; although in many cases, reasonable routes have now been withdrawn.