Oddly we've had
another thread within the last week of someone using a 60+ Oyster Card at Bethnal Green station.
I wonder if the inspector believed your story, and was trying to do you a favour here. There are two different sets of law you can be prosecuted under: the Railway Bylaws (specifically Bylaw 18) and the Regulation of the Railways Act. The Bylaws make it illegal to travel without a valid ticket, whether deliberately or by accident; the Regulation of the Railways Act makes it illegal to deliberately evade your fare. A Bylaws prosecution has a much lower fine, and should never appear on a DBS check.
So while you would still probably be guilty of a Bylaws offence if you have been using the Oyster card to travel, you wouldn't be guilty of an offence under the Regulation of the Railway if it was genuinely accidental. However, if you try and defend yourself with this claim then NajaB's question - why did you have your mum's 60+ Oyster - is an obvious one that will be put to you, and I'd have thought that the prosecution would look to test your explanation very robuslty in court.