The relevent condition is:
"If the ‘Route’ also states ‘and Connections’, travel is allowed on appropriate connecting trains where shown on the ticket(s) or other valid travel itinerary."
http://www.nationalrail.co.uk/times_fares/advance_conditions.html
Now in the case of Leeds-Sheffield, the Northern services are non-reservable, so if you are initially 'booked' on one of these, if your ticket is on standard orange ticket stock rather than the airline style stock, no connecting train will be shown on the tickets. Therefore, we need to refer to an 'other valid travel itinerary' and in order to do that we need to determine what one is.
If you book over the internet or at some booking offices, you are given an itinary either with your ticket or in a booking confirmation. As this came with the ticket, this must surely be a valid travel itinerary.
Now, those people who are arguing that the ticket is valid on Cross Country services whether a reservation is issued or not are relying on an itinerary derived from an internet based journey planner being a 'valid travel itinerary'. Certainly it is a travel itinerary, but whether it is valid with such a ticket is not defined anywhere, thus it is certainly not clear cut. I suspect that some of the Cross Country guards who decline such tickets are doing so on the basis of the only 'valid travel itinerary' being that provided with the ticket. I think there is a decent argument either way, the only way to get a definitive answer would be for this to go to court or for ATOC to revise the conditions to clarify the issue.
Incidentally, even when I have had a reservation on a Cross Country train in those circumstances, I have had an argument as the guard believed that connecting services could only be local trains with no reservations. He quickly lost the ensuing discussion.