We also haven't had confirmation that she explained her disability and whether she backed that up for showing the relevant cards. If she did then I would agree that the appeal should be successful and moreover that a complaint should be made. Clearly if she did neither then the Inspector wouldn't have had any grounds for treating her any differently to a normal traveller.
IMO an appeal should succeed whether or not either of the two things you’ve stated. A complaint probably wouldn’t be warranted if not though.
There is no requirement to provide any specific documentation or card to prove your disability when requesting reasonable adjustments. Proof of disability can be required but this must be reasonable and proportionate.
The duty to make reasonable adjustments is anticipatory, and I wonder whether compliance with the Equality Act in this scenario might actually involve asking if the passenger has any relevant disability before taking any action other than selling a ticket, rather than relying on the disabled passenger, who may have disabilities affecting cognition or social interaction, to mention it.
NRCoT says you may board a train without a valid ticket if:
You have a disability and Ticket purchasing arrangements at the station where you started your journey were not accessible to you.
No specific documentation is required for this term to be applicable, only that the passenger is disabled (presumably under either one of the plain English meaning or the Equality Act definition).
