They sound rather unlucky! Must have encountered a keen guard or TTI. How did they achieve '3 fails' exactly? You'd be rather unlikely to have your 'piece' checked 3 times in that short distance. Surely if they had offered to pay they could have avoided the encounter with the BTP, unless they were carrying no cash which is not recommended if you're not valid.
The 3 fails:
1. Failure to produce a valid ticket when asked to do so by an authorised person
2. Failure to purchase a ticket valid for the journey being undertaken when offered the opportunity to do so
3. Failure to provide appropriate personal details (for reporting purposes)
When I was trained I was told never to bother BTP with an alleged fare evader without first satisfying those three conditions.
Yes, purchasing a suitable ticket would certainly have avoided any BTP involvement but they simply refused to accept they'd been rumbled. I suspect the passenger simply didn't think the actual validity of the rover would be known by any frontline staff. The line "Heart of England must be valid anywhere in England" was priceless! As for the guard involved I believe they were an enthusiast so possibly had better knowledge of rover tickets than many of their colleagues. My own training was not to argue about validities I wasn't sure about.