The way I see it,
@AnkleBoots' #10 asks why a person convicted of a fares offence would admit it to their employer if the general question about having convictions was asked. This isn't a situation where such a person would be incriminating themselves by answering, so they have no right to say nothing. Unless
@AnkleBoots is actually saying the response should be "no comment", the person can either be "up front", as
@ForTheLoveOf suggested or they can lie about having the conviction. In that case, I couldn't disagree with you when you say "lying rarely, if ever, helps", even if "[the employer] would not otherwise have found out".
But that moved swiftly on to #11, and the question of whether the same person should have made admissions to the RPO. Here, because the RPO's investigations could lead to a criminal prosecution, the suspect had the right not to be obliged to incriminate themselves (the RPO should also have made the suspect aware they have this right) So when
@AnkleBoots suggests that the suspect shouldn't have made the admissions, it is not to necessarily suggest the suspect should have lied and e.g. said that it was the first occasion they had used the pass. Replying "no comment" or "I can't answer", if the direct question is asked, isn't lying, it's refusing to answer, which is the suspect's right. Not mentioning previous journeys if the direct question isn't asked, certainly isn't lying.
Lying, when being questioned under caution, rarely turns out to be helpful. Declining to answer can sometimes be helpful to a suspect, e.g. if it allows them to obtain proper legal advice about what the consequences would be if/when they do answer the questions. Of course, a consequence of refusing to answer a direct question when asked, but then giving a convenient explanation at trail, could be to create an impression of dishonesty in the mind of a jury. Conversely, trying to answer every question as fully as possible can often be unhelpful. If, e.g. a suspect tries to be honest, but makes a mistake and volunteers information or answers a question in a way which can later be proved to be false, the accusation; "You lied when questioned and you are obviously lying now" can be thrown at them if they give evidence in their defence.
So there will be cases where responding "no comment" to a particular question would be the right thing to do, others where it wouldn't, yet others where volunteering information would be helpful, some where doing so could be disastrous. But even if that was this forum's remit, are posters here necessarily aprised of all the relevant facts to be able to offer such advice on a case by case basis?
Apologies for the long post and to the OP for taking the thread away from discussing their case specifically.