Unfortunately, if the matter was not regularised there and then through the purchase of a new ticket (or the issuance of a Penalty Fare), there would be no defence to a prosection under Byelaw 18(1) of the
Railway Byelaws 2005, which creates a strict liability offence of boarding a train without a valid ticket.
There would be a defence under Byelaw 18(3), as the guard has permitted him to continue his journey without a valid ticket.
The guard would have been well within his/her rights to have treated the passenger as travelling without a valid ticket, and required the OP to pay for a full-fare ticket there and then, but by permitting the OP to continue the journey without a valid ticket the guard has invoked Byelaw 18(3). And quite rightly, when presented with the necessary information, the TOC has decided there are no grounds to prosecute.
I think the main issue here is that the OP was obviously upset by the letter he received. The wording of the letter clearly gave the OP the impression that the TOC were about to prosecute, whereas in fact the TOC were only asking for the OP's version of events, and giving him the opportunity to pay if payment was owed (e.g. if he didn't in fact have a valid railcard at home), before deciding if there were grounds to prosecute. This is not the only case where people have got this impression, and I think these letters could be made clearer. Unfortunately, as they are the first step in the legal process in cases where the TOC does decide to prosecute, they may have to be written in "legalese".