I believe the shortest route is actually "the shortest route over which a passenger service normally operates" or somesuch. I think one day a week would be seriously pushing that definition (though it's accepted for "no Sunday service" routes*). In cases where you have an infrequent service over a shorter route, the Any Permitted normally includes the "normal" route (and is priced up a bit as a result) and you get a routed ticket (route DIRECT, quite commonly) for the shorter one. I believe this applies to the likes of Stockport to Stalybridge at least.
* Though in BR days Ormskirk to Preston via Liverpool was accepted on a Sunday despite causing a whacking fares anomaly.
There is some ambiguity as to the meaning of "shortest route". The NRCoT (which is where the most unrestricted right derives from, as negative easements only apply to routes deriving from the Routeing Guide) says:
any services (including any change of trains) over the shortest route which can be used by scheduled passenger services between the stations shown on your Ticket
It is unclear whether "which can be used by scheduled passenger services" refers to the capability of the
route to be used by passenger services (e.g. is it signalled to passenger standards and so could a passenger service theoretically run?) or whether it refers to the capability of the
passenger to use the route by passenger services (e.g. are there any train services over it). Personally I would have thought the latter interpretation would make a lot more sense, and is more likely to be the intended meaning. The use of the epithet "scheduled" also suggests this is the case (as passenger services do not need to be scheduled to be able to use a particular line).
Any other interpretation would also mean that a route
theoretically capable of passenger operation must be considered to be the shortest route, even if there are no scheduled services. For example the shortest route from Rugeley Trent Valley to Burton-on-Trent is (by a very small margin) via the Lichfield avoiding curve, but I don't think this has ever had a passenger service. Certainly not for many decades. Similarly the shortest route from Cricklewood to Acton Main Line would be via the Dudding Hill line, but this has never had a regularly scheduled passenger service either, AFAIK.
The phrase "can be used" also suggests that account must be taken of the timetable. If there is a train service over a potential shortest route, but it doesn't run on the day you buy your ticket (as in this case), I don't see that it really has any relevance - any more than it would be relevant today that there was an hourly service between Glenrothes and Kirkcaldy right up until 2 days ago.
That in turn opens up a further can of worms - what if the last train of the day over the shortest route has already left, by the time you buy/use your ticket? But we can keep that can's lid largely shut for this journey, as there are no scheduled services which could use if you buy your ticket on a Saturday, or buy an Off-Peak Day Return. The issue of there being a service over the shortest route, but it not calling at the station(s) you are travelling to/from (e.g. Rugeley to Stoke via Colwich) is also another can of worms which we can leave for another day!
The
Routeing Guide Instructions uses a slightly different interpretation for the shortest route, simply referring one to the electronic National Rail Timetable published by Network Rail. In some respects this is helpful, as not all routes have mileages listed in this timetable; if a route is not listed then obviously it cannot be used in the determination of the shortest route - thus meaning a longer route could potentially count as the shortest route. But in this particular example it is of little assistance, as a mileage is still listed for GLT-KDY - understandably so, given there is still the Sunday and once each way M-F service.
Meanwhile the
Routeing Guide In Detail uses the phrase "shortest route served by a regular passenger service", the letter of which a once-weekly or even once-yearly service could be seen to satisfy. So it is of little assistance, other than in additionally allowing a route no more than 3 miles longer than the shortest route (but again, there is no such route for GLT-KDY).
Overall the position is somewhat of a mess - in practice the impact is simply going to be that booking engines won't be able to sell tickets unless they split, but on the ground I cannot see that any guard or other member of staff would object to one travelling via Markinch. What other route could they possibly suggest?