However the decision cannot be abritrary and fail to consider relevant matters when reaching a decision they have reasonable suspicion.
There’s nothing arbitrary. If you fail to provide a name and address the police get involved.
A customer traveling on a Bank Holiday asking to buy a ticket available and advertised on the company website as available on Bank Holidays and telling the guard one of their colleagues confirmed it could be bought on board ought to be enough to cause the guard to pause for thought and consider whether they have a reasonable suspicion.
I don’t think you understand what’s meant by reasonable suspicion in this context.
The guard doesn’t have to evaluate every single possible defence. There’s a world of difference between reasonably suspecting someone and actually thinking they’re guilty.
With the police, a Constable only has to “reasonably suspect” me to have committed an offence to detain me.
For example, if I had a crazy girlfriend she can go into the police station and say I hit her, show them a bruise, and an officer might reasonably suspect me to have committed that an assault. They then turn up and arrest me, the purpose being to conduct an investigation. There are a myriad of defences available to me against that allegation, and the police do not have to work their way through every possibility before deciding whether to nick me.
Now apply those principles to a guard on a train; the threshold will certainly not be higher than the police.
In the situation the customer had:
The wrong ticket
AND
Unwilling to pay the Upgrade (properly) due
AND
Only has an uncorroborated excuse
...then yes. The guard has reasonable suspicion that the person has committed an offence, and may ask for their details. The purpose of which is to invoice them, which is civil, can be (and in the case in the OP), would be challenged.
We are only talking about taking someone’s details so the matter can be sorted out properly afterwards, not locking them up.
In the situation being considered it isn't the customer who is unwilling to pay, but the guard who is unwilling to sell the ticket their colleague has said can be purchased.
*Allegedly* said can be purchased, with no proof to back that up.
It is also the customer refusing to pay.
But in this scenario it has potentially creating a criminal situation by the guard refusing to sell the ticket.
A guard refusing to sell a ticket doesn’t cause a criminal situation.
Not paying for the upgrade as asked, and not giving your details are what make this a criminal situation.