If I was on PlusBus I would expect the bus journey to be covered in the event of delays. A journey by LU would also surely be fine if the ticket was from somewhere like U1, or a Travelcard, or similar. I do not think the mode matters, it is the ticketing that matters surely?
If I was on a non-railway ticket product then I would hope that common sense would prevail, and this did happen to me once when a bus was very badly delayed, I think the York races were on earlier and I therefore had to wait approx 1 hour for a bus (it would have been quicker to walk). However is there a contractual right to demand that the railway ticket(s) should be honoured on later trains due to a delay on a different mode of transport that was taken with non-railway ticketing? I would love to say "yes" but sadly I can find nothing that indicates that is the case. But should it be? Of course it should!
I do not think that TOCs can get away with saying "that train is run by a different company", if they are a member of RSP they are required to honour all tickets that are of relevant route on their services in accordance with the conditions. These "but Northern adhered to their part of the contract by eventually getting you to the place stated on the first ticket, and Virgin are not obliged to honour your ticket because Northern caused the delay" excuses that I've seen on here before are nonsense IMO.
Once you start your journey on a rail ticket (this could start with a bus, tube, etc) I firmly believe that the rule that "if you are delayed while travelling..." applies and the only logical interpretation is that it overrules the rules that you can only get the booked train(s). I believe this must, surely, apply regardless of the mode on which the delay is experienced.
Grey areas may be: Combining tickets to London Terminals, where the tickets do not join at the same London Terminal (does the fact the named station grouping is the same, mean that it does count as covering your entire journey under Condition 19? I'd hope so!), combining PlusBus tickets on different routes (e.g. York - Radlett Plusbus, Watford Plusbus - Rugby); the plusbus areas overlap and both include Aldenham). I would say these should be fine, but I could see some staff arguing otherwise.