The discussion had moved on to a question about the legality of
them demanding a ticket check from someone that they had seen
come out of an 'exit only' route (you seem to have snipped this bit
and returned only to the original question). As they would not
know if the person had an Oyster at this point, how could this be
a reasonable thing to do?

Indeed. In a station with a working gateline it would be legal for ticket
checks to be carried out outside the gateline but probably largely pointless
on the whole. So the ticket checks at Kings Cross described by Jonathan
earlier must surely have been targetting something unique about Oyster use,
or more likely misuse. Like him I can't immediately think of anything
unless there is widespread abuse, or accidental misuse, of Oyster PrePay
where they don't touch in to the system. I believe that still only results
in a minimum fare doesn't it?