If you arrived at a station and were told by the ticket office staff that they had a machine fault and you should buy on the train (something that has happened to me more than once), and you then got on the train and were asked for your name and address and then were later prosecuted, would you go along with that because "prima face" you had broken the Byelaw?
First of all, I don't "go along with", let alone "argue strongly in favour of" TOCs prosecuting in situations where a passenger claims that he is travelling having been given verbal permission to do so. I haven't argued in favour of prosecution, simply that because boarding a train without a valid ticket is a slam dunk offence of strict liability, where a passenger cannot show a ticket or evidence of being given authority to travel, there is a clear risk of being prosecuted. Of course the honest passenger would expect to be believed, but the TOC has to at least consider the possibility that the passenger is a fare dodger who is spinning a tale of being given verbal permission as explanation of being found ticketless. I notice that you haven't explained how the TOC can use the good judgement you expect them to apply, to differentiate the honest passenger from the fare dodger.
What I am suggesting is that the current system of verbal permission is flawed from the passenger's point of view because the issuing of authority to travel without a ticket isn't documented or traceable. If a passenger's explanation of being given verbal permission isn't believed, without evidence of being given such permission, they are indistinguishable from a fare dodger telling a tale.
In the example you give, if I approach the conductor on the train and ask to buy a ticket, he is likely to ask why I didn't purchase at the station. I then tell the conductor that I was told to buy on the train by the staff member at the booking office as he could not issue the ticket.
What happens then depends on how believable the conductor finds my reason for boarding without a ticket. In the example you give, as it is a simple matter of checking whether the booking office was unable to issue the ticket, one would hope that the explanation would be accepted and there would be no question of prosecution.
But what should happen in a less clear cut situation? A passenger has a ticket for return travel to Reading, routed "not via London". He arrives late at the station and misses the "not via London" train. On enquiry to a member of staff on the platform, he's told the next train to Reading is via London and in the belief that he's been given authority to travel, he boards the train. When his ticket is checked on the train he refuses to pay an excess fare, arguing strongly that he was given verbal permission to take the "via London" train to get him to his destination.
The passenger has an honest (but probably mistaken) belief that he has been given authority to travel. The TOC sees a passenger traveling on an invalid ticket, refusing to pay the correct fare.
Does the TOC give the passenger the benefit of the doubt and waive the demand for payment of the excess fare?