I disagree. The original question was in respect to people choosing to split their journey:
In the example you mention, there was no choice and no choosing.
The original question applies to any
journey where a
connection is being made, and the passenger is choosing to purchase
a combination of two or more tickets for the one journey by making two separate queries of a booking engine, to and from the change point.
The question applies equally to a journey such as:
1543 Appleby - Leeds (arr 1738)
1749 Leeds - Middlesbrough (1914)
The TOC's websites require customers to do:
1641 Appleby - Carlisle (arr 1728)
1838 Carlisle - Newcastle (arr 2017)
2030 Newcastle - Middlesbrough (arr 2148)
The fare charged by the TOCs for the longer journey via Carlisle/Newcastle is £33.10.
Passengers can take
sheff1's advice highlighted by me in bold above, and book through an accredited website that offers a combination of fares for one journey (colloquially known as a "split ticket" website; the informal language used not important) and pay £36.70 for the faster journey on flexible tickets, or pay £24.40 for fixed time tickets and be issued one booking reference , one itinerary and all relevant fares in one transaction.
Or they can do as
trainophile says and put two journey queries into their basket using a TOC website, and pay £11.50 for the Appleby to Leeds ticket followed by £12.90 for the Leeds to Middlesbrough ticket, and as
trainophile says, passengers need to manually verify that the 11 minute connection in Leeds is a valid connection, which it is.
People have posted advice on where to verify that the connection is a valid one, and people have posted advice on how to avoid the requirement to manually check by booking through a website that will book all required fares for you.
For South Milford to Bridlington, passengers could choose to purchase a combination of fares, or if they do not choose that, I would imagine the Guard would make that suggestion anyway. I do not see the relevance of "choice" or the argument over the informal term "splitting"; none of that matters!