"My mother sang Dance To Yer Daddy"
If she'd sung 'Your Tiny Hand is Frozen' to you, would that make you an opera singer?
"By which she means she is less concerned with a song's provenance than its quality"
This is a sweeping generalisation which depends on which singer or musician you ask. The older musicians and singers around here used to make a point of telling you which songs, tunes, ways of playing/singing were or were not 'traditional. Walter Pardon proudly and often publicly declared which of his songs were 'folk', and went into long explanations on the difference between them and the music hall, Victorian, 1920s pop songs.
Suggest you read what he had to say in articals 'The Other Songs' and my reply on the Musical Traditions site archive.
In the end it has nothing whatever to do with the definition of a traditional singer.
Jim Carroll