I am sure the EC TM on our train home on Sunday said a good two or three times, in a very clear fashion, that passengers with advanced tickets needed to check the date and the time matched the service which she read out (to make it perfectly clear and easy to match-up) and warned that any ticket that was not for that service would result in a totally new ticket being sold and the existing one being invalid and worthless.
That's EC, but surely Virgin says much the same?
Now, I can say that on my last trip with EC I nearly did board the wrong train. We'd walked down the platform (3?) at York to be in the right section for our booked seats and the previous train was delayed. Where we stood was away from the screens and not close to the speakers, such that a lot of people boarded. I asked staff who said it was the earlier train, so we got off. A lot of people probably didn't - but who knows if they were waiting for that, had open tickets or would get 'caught'.
However, given the circumstances (the delayed train arrived almost to the minute 'our' service was due) I would hope that EC wouldn't have done anyone. The worst that would have happened was people not being able to sit in their seats occupied by someone else.
I am sure if records showed a Virgin train arriving at the exact same time, discretion could be used then too - but it seems that didn't happen.
In other words; tough. That's why advance tickets are cheap. Try doing the same thing when you miss your Ryanair flight, or even arriving early and assuming you'll get on an earlier flight. At best you'll pay the excess, plus a booking fee, but you certainly won't blag it.
Having read some of the comments, it's quite ironic that they moan about the fares varying so much - while making comparisons to flying. Er, hello! The reason fares vary so much, as against a nice simple single fare, is that the train companies operate JUST LIKE THE AIRLINES. And the airlines don't let you change flight for exactly the same reason.
If all advance tickets were scrapped, there's a chance the walk-on fare could be lowered a bit but not much.. and then we'd ALL be moaning. It's crazy to think that an advanced ticket with a seat reservation could be used on another train, any more than you could decide that you paid for a £20 ticket (for example) but then decided to go somewhere completely different, with a different operator, perhaps on a different day (but also costing £20) and you refuse to pay because you have totally invalid tickets worth the same amount that you didn't use.
hock
and the only time a "genuine mistake" would not apply is if either adult had been a known, long-term commuter, railway employee or enthusiast. 
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