Would the guard/RPI accept the scrap bit of paper with a few letters/numbers written on (and presumably have no way to check the validity of it)?
And what could stop people who couldn’t collect Anytime tickets from collecting and using them later?
To what extent should I expect this to not be as straightforward as I'd hope?
While I appreciate that you all clearly had the best of intentions, these really are the wrong questions to be asking.
It's easy to get into a rut if you read the forum a lot of thinking 'will they believe me?' or 'How can they check?'. Turn the situation on it's head. Whose problem is it if an RPI thinks you are not telling the truth if you are advised to board a train and travel with a
reference number (not an email confirmation, a reference number, I would make that distinction during my conversation with station staff)? Yours? No. It's theirs.
If you're given verbal permission to board, that's adequate. You don't need to do anything else to demonstrate that you have the right to travel, except present your reference number of course, if that was a condition of boarding. How can they prevent fraud? In all manner of ways - it remains illegal, of course. It's not the customer's consideration.
In the unlikely event that this happens and you're forced to buy a new ticket, I would recommend refusing to hand over any money. Of course, you may need to give your name and address (and nothing else) and should probably do so if asked.