So she went from some unspecified station to London Bridge, and at that station entered the barrier using a paper travelcard. She arrived at London Bridge and realised that her travelcard did not cover her for that station, either before or after attempting to use the travelcard. (Perhaps it was a zone 2-6 travelcard, whereas London Bridge is zone 1) She then exited using the PAYG Oyster card. Is this correct?
What would have happened is that the PAYG Oyster says that there is no entry somewhere else, so there is no way of telling where she has come from, so she is charged a maximum fare, which I think is £7.80.
So she would have had £3.80 balance on the card, minus a £7.80 maximum fare, leaves -£4.
Ok I don't think that would work. The 18+ Oyster Card is a form of identification giving her a discount off a paper travel card. If she buys a paper travelcard using the Oyster Card to prove she is in full time education and therefore entitled to a discount, there would be no record of the purchase on the Oyster Card - the Oyster Card is just ID in this case, the same as my driving licence is ID when I buy a bottle of vodka, and no record is stored. The paper travelcard is essentially 'cash', and if you lose it it's gone, and it's very hard to prove you ever had one.
The question is why didn't she simply get the travelcard loaded onto the Oyster Card? That would be simpler, there would be a record online and she'd be able to get it revoked/replaced if lost. I don't see why you would want a paper travelcard when you've already got Oyster. It would be more expensive, e.g., when travelling outside her paid for zones.
As it is the only way she can prove that she had a valid ticket would be something like credit card records.
Did she pay by debit/credit card?
The London Bridge journey happened somewhere between Jan and Feb 2012. This particular offence happened early April. She cant recall if she paid by debit card for the original travel card or not, she is headed for the bank to check if they can find any record of that. But then again even if we did have absolute proof she purchased the travelcard, it doesn't prove she had it with her on the day in the station itself. All it proves is that she purchased a paper ticket once upon a time.
In regards to your other questions (criticisms), I have no idea. I'm too tired to further question her. She's evidently guilty of making such silly mistakes. She uses her Oyster to purchase paper tickets when there are ticket machines at the station that do the 18+ discounts automatically if you have the right card. When I made this point to her, she said she didn't know.