On that basis... Why have the thing about people having to wait for the next train from the booked operator at all? Why not just have a simple policy that if you miss a train due to a late connection, you board the next train to your destination regardless of operator. It would remove this ambiguous situation and improve people's general perception of rail travel.
The thing is that apart from your scenario - which i doubt anyone at Scotrail would object to letting you get on the next service - is that most places that may have on or more TOCs serving it - lets say Preston - then theres quite regular tiemtable by both the intercity TOCs that serve it so i dont think it would be, there, unreasonable to wait for the next train by your TOC. Unless of course its late at night and only one more train to go or some other scenario that i cant think of off the top of my head.
And as many people have said - speaking to the guard will always get you an answer - whetehr its the right one or not is the hard part to guess but its their train.