It’s more likely that the ducklings adopted her. She doesn’t have to feed them, so there’s no great urgency to chase the extras off.
Yes, precocial birds. The Great Grandma explanation makes sense. There’s an old video about Konrad Lorenz and his studies in imprinting; this may be it or part of it:
https://www.youtube.com/watch?v=IysBMqaSAC8