As a matter of explanation I had this out with London TravelWatch a few years ago. Basically, the Single Fare Finder is the DEFINITIVE way of working out fares: not the Tube Map.
I have attached their reply (about Hoxton Z1/2 to Stratford International DLR Z2/3) because it is instructive. However bizarre the reasoning, the Single Fare Finder is always correct.
Dear Mr Butterworth
0294556 - TFL ticketing information issue
Thank you for your enquiry.
I can understand your frustration with the responses you have received from Transport for London, which were initially obviously incorrect.
However, we have looked into the information on TFL’s Single Fare Finder and it does appear to be correct. Since it does give both the cheaper and more expensive fares and advises passengers to touch in at Stratford when taking the cheaper route.
This information is correct because, if a passenger travelling from Stratford International DLR did not validate their Oystercard when ‘interchanging’ at Stratford, then TFL’s system would automatically assume that they had taken the more expensive route through Zone 1 to Hoxton and charge the higher fare. That is to say, it would assume that the passenger had approached Hoxton from the direction of Whitechapel and Shoreditch High Street station, which is in Zone 1, and not from the direction of Dalston Junction and Haggerston, which are in Zone 2, and therefore on the cheaper route.
TFL could, of course, have explained this more fully rather than more or less asserting that they were right about it and leaving it at that.
I hope that this clarifies matters for you.
I even coded up a version of the network using Dijkstra’s algorithm in PHP just to prove the Single Fare Finder is highly inconsistent: here’s a Excel Sheet - https://ukfree.tv/styles/images/2018/Data%20based%20on%20SHORTEST%20tube,%20rail,%20OSI%20from%20Charing%20Cross%20station.xlsx and an image of what I found about the fareness of the Zones …