"Of course it is impossible to draw a line between folk songs and other songs "
Not in the slightest
Not only are folk songs well defined, but there is over a century's documentation covering what they are and where they came from
The misuse of the term, basically deliberately so, is a comparatively recent phenomenon and has no research to back it other than "folk song is what I choose to consider it is"
A self conscious manipulation of the term makes no difference to the existing definition (much in need of up-dating based on what information has been gathered latterly) makes not an iota of difference - until a new definition is reached and accepted generally, the one we have serves very nicely, thank you.
As Mike points out, narrative is just one type of song which doesn't include, say, shanties, lyrical songs, ritual pieces, skipping and ball games...... and songs with verses which don't ecesserily relate to one another.
Jim Carroll