I am a bit perplexed as to how you come to this conclusion? Nantwich has a TVM which would have been the OPs first opportunity to buy a ticket. The TVM may not take cash but since the OP subsequently bought his weekly ticket with a debit card then the TVM would still have been his first opportunity to buy in his particular circumstances.
As it said ATW's wording is different and doesn't suggest that you can buy on board. However, if it was a Northern station and there was a queue for the TVM someone could think Northern say the conductor will sell you the standard fare on board and it's before 09:30 so I can buy the ticket I want from the conductor.
There's all sorts of grey areas with TVMs:
1. It might not sell the ticket you require.
2. It might refuse your card for no apparent reason.
3. Passengers charters state how long you should be expected to queue to buy a ticket. If the queuing time exceeds that time that surely you can argue that it wasn't an opportunity to buy a ticket.
4. As well as what I said regarding Northern many TOCs like TPE refer to 'walking past an open ticket office' in announcements and ignore TVMs.
5. The TVM might crash but still show the green 'working light' - it happens on Northern TVMs.
In the OP's case they showed an invalid ticket rather than initially saying they don't have a ticket, which would likely affect their claim that they would have bought a ticket if given the opportunity. If they failed to realise the ticket had expired then why would they have purchased a new ticket?
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Unfortunately, it's not clear how and when that "someone" is going to articulate that argument. To the Inspector when detected travelling without a ticket? To the Investigator reading their written explanation of events? To the Magistrates when facing the risk of Conviction?
In each of those circumstances we've seen persuasive arguments fail to persuade, and we have no binding authority to support that "someone" against the other compelling interpretation - that they were evading paying their fare by only offering to pay when challenged.
I think a good solicitor could win a case of fare evasion on that argument. However, I doubt many good solicitors appear in court for cases of over unpaid fares of under £10 unless it's the solicitor themselves accused of fare evasion.