We suspect that it's the sort of tune/song that school kids were taught to sing and to play on recorders at that time and so is meant to convey an influence from her childhood.
The people from the Oamaru/Dunedin/Otago area tended to have a Scots background anyway so maybe it was a song Janet knew - was it mentioned in any of her books?
I read 'Owls do cry' many years ago but can't recall if there was anything vaguely related in it.
It may simply have been a choice made by the TV Producer.
Robyn