Narrative painting, for me, is not the same as illustration. Illustration requires the written source or the specific story it is depicting, whereas narrative painting doesn't. Narrative painting can have quite random images in it without any intended connections or meanings by the artist and still every viewer could invent a story to goalong with the painting in an attempt to explain it.
Here is a quote from Peter Heehs to illustrate my point:
"Narrative, indispensable for ordering events in time, can also be used to give unified meaning to forms in space. Most people shown a figurative* picture can without difficulty invent a story, often elaborate and original, about what is happening (often with reference to what has happened and will happen) to the figures. ... Adults looking at a painting in a book or museum frequently invent narratives of this sort to explain to themselves or others what the painting is about. ... ...it can also be done when the painting has no obvious narrative intent. Whatever the subject of painting, viewers make use of plotted language to explain its meaning to themselves and others."
1995. “Narrative Painting and Narratives about Paintings: Poussin among the Philosophers.” Narrative, vol. 3, no. 3, 211–231.

*by Heehs' quote it seems to me as if the only restriction on this idea is the fact that the picture has to be FIGURATIVE - in some way present images that are comprehensible to the viewer.