I agree with John. I think in this case it is also useful to consider clause 19 of the conditions of carriage, which states:
"19. Using a combination of tickets
You may use two or more tickets for one journey as long as together they cover the entire
journey and one of the following applies:
(a) they are both Zonal Tickets (unless special conditions prohibit their use);
(b) the train you are in calls at a station where you change from one
ticket to another; or
(c) one of the tickets is a Season Ticket (which for this purpose does not include
Season Tickets or travel passes issued on behalf of a passenger transport
executive or local authority) or a leisure travel pass, and the other ticket(s) is/are not.
You must comply with any restriction shown on the tickets relating to travel in the trains of
a particular Train Company or Train Companies (see Condition 10).
If you do not comply with this Condition, you will be treated as having joined the train
without a ticket and the relevant parts of Condition 2 or 4 will apply, either to the entire
journey, or from the last station where the train stopped at which at least one of the
tickets was valid."
http://www.nationalrail.co.uk/system/galleries/download/misc/NRCOC.pdf
Now as Gus is travelling through from Peterborough on a seperate ticket, this now means that he is defined as making one through journey from Peterborough to Kyle. Now there is only one through journey from Peterborough to Kyle, which departs Peterborough at 08:46 on a weekday. As Gus wishes to travel on the 12:47 departure from Peterborough, a whole 4 hours after the journey which can be completed in one day, I think it is entirely reasonable that it is a journey which cannot reasonably be completed in the day, so the overnight stay for connectional purposes is appropriate.