Thanks to all. Before seeing this record, I'd always assumed that "son of..." applied to males before the age of majority (either 16 or 18 or 21) and after that their parents were not named (whether or not the man was married, though I have seen "married man" in some burial records).
(I'm not sure about females in this context. Mostly they seemed to move from being "daughter of" to "wife of", consistent with the customs of the time. I've even seen "wife of X" without her being given a name - hard to understand from our point of view.)
Back to John Kilner: as one of you suggested, I've now looked at all the burials at St Nicholas', Cumberworth, in the batch that Ancestry gives us. There are only six pages; the earliest burial is on 27 November 1831 and the latest 6 January 1833. I've listed all males aged 21 and over (in order of age, not date). All entries are signed by G.B.Dunn.
PARENTS IDENTIFIED
George Lockwood, 21
Joseph Shaw, 23
Henry Hinchliffe, 25
George Wood, 26
John Kilner, 39
PARENTS NOT IDENTIFIED
William Turton, 47
Joseph Senior, 55
Richard Lodge, 60
Abraham Woodhead, 83
Rev Dunn may have been using a rule that added parents' names for men up to the age of, say, 40, and John Kilner fell just on the right side of the line.
I had wondered if parents were named if they were still alive (so that older men would be less likely to have living parents) but I believe - not entirely sure - that John Kilner's father had died by 1832 so he wouldn't have been named under this rule.
I guess my question is now: has anyone heard of an age other than 16 or 18 or 21 being used as a cut-off in this way? Such ages were usually associated with property laws (age of majority and so on), and I've never heard of 40 being a significant legal age in any other context.