This is a reasonably common thing - for example the law also assumes letters are delivered after being posted unless there is evidence to the contrary.
If the computer says money amounts don't match, that still doesn't say who stole it.
It could have been the person directly responsible for it -- or it could have been a third party attempting to steal from them, or someone hacking the system, etc.
You still need to go beyond reasonable doubt -- establish motive, establish corroborating evidence, etc.
Of course they can claim anything they want, but it could have weakened their argument considerably. As a defense lawyer I would have asked for those numbers to raise some doubts, not because it's incontrovertible proof.
Clearly they did not have to do these things.
In addition, the Horizon system only offered the accused the "client-side" data, so to speak - they could see what they had inputted and what the system had printed out. They couldn't see any kind of internal transaction data, or what happened to the data once it was inputted. Post Office repeatedly obstructed attempts of the accused, their lawyers, and even the third-party auditor they hired to examine the system for faults to retrieve that data - likely because they knew that handing over that data would immediately show the flaws in the system.
The whole thing just stinks of corruption, to be honest.
We need better frameworks for incorporating doubt into our thinking about such things... whether it’s the reliability of computers, or of the justice system, producing what we expect.
They did not invent registered mail for nothing. It is exactly for the reason that mail does not get delivered. I am sick of counting how many times I've received somebody else's mail. And I got $8,000 worth of integrated circuits from Digikey marked as delivered but missing. By sheer accident found that it's been delivered to the house of one of my neighbors.
I even once chased the postman and asked him why are you dropping somebody else's mail in my box? All I could get from him was: "it is ok"
Using proof of delivery can cause problems. People are allowed to decline to accept those letters, and if they do that there's now a paper trail proving they didn't get your letter. That doesn't happen if you just use proof of posting.
Then it is sorry state of affairs. People could get punished for no fault of their own.
You need proof of posting, not proof of delivery. If you can prove posting, it’s up to them to disprove delivery.