I think there is not going to be any single 'right' answer here.
I would reject any argument that the tickets "don't join up"; they clearly do (at London Terminals)
But it's true to say that a through itinerary cannot be generated, at the time the passenger made the journey, without using the "TUBE" fixed link.
Without knowing what the booked and actual arrival/departure times at the respective London Terminals were, it's difficult to comment.
But this does highlight an issue that I've recommended for a long time: I strongly recommend using a National Rail accredited retailer that offers split tickets; you will be provided a valid through itinerary, and be fully protected in the event of delays, or changes to the timetable between the dates of booking and travel, as well as (I'd expect) support from the retailer if required. I would then suggest sticking to the itinerary, unless specifically advised not to.