Failure to show a ticket or other authority to travel is a strict liability matter. All that needs to be proven is that no ticket was shown. No intent must be proven.
If an authorised person gave you permission to travel on the service with the ticket you were holding, then that ticket
was a valid ticket (or at least, as you put it, "valid authority to travel in lieu of a ticket"). This has nothing to do with intent.
Saying "I don't have a ticket but the man on the platform said it was alright" still leaves the burden of proof on the passenger to supply evidence of that authority to travel.
Again, I am not an expert on English criminal law. But I find it hard to believe that in a criminal case the burden of proof is ever on the defendant (with the possible exception of insanity defences and a few other things for which a specific statutory framework has been set up). My understanding is that if a defendant raises a defence such as "my ticket was valid because I was given permission to use it by an authorised person", and provides prima facie evidence in the form of his/her own statement under oath, then the burden shifts to the prosecution to prove, beyond a reasonable doubt, that this didn't happen. In practical terms, the way they would do this would be by attacking the defendant's credibility and persuading the magistrates not to believe him/her. So from a practical standpoint, the defendant still faces an uphill battle if using a defence along these lines (which is unfortunate if the defendant is telling the truth). But legally, I believe the burden of proof still rests with the prosecution.
What you and others seem to be suggesting is that in all cases, a strict liability matter such as this can be successfully defended by simply stating that an authorised person had allowed travel, and that you don't even need to provide proof of that authority, and it is up to the TOC to prove that authority wasn't given. That's not correct. The burden of proof is on the passenger to supply either a ticket or evidence of a valid authority to travel in lieu of that ticket.
(Emphasis mine.)
The defendant's statement under oath is sufficient proof if the magistrates find it credible.
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That has to be done in a criminal prosecution anyway, regardless of whether "strict proof" is claimed.
Well, sometimes a defendant will admit (to save trial time and expense, etc) basic details like identity or location (which might be relevant to jurisdiction). Putting the prosecution to strict proof on every element could be taken to mean that you are not admitting anything, even these basic details.
