Based on the bird behavior it would be closer, yeah.
Looking at the etymology, it seems the middle English just used the word for the whole situation, and not a strict analogy.

For pure bird-ness, it would apply best to a case of a woman adopting a step child, even more to adoption, and most of all to a single mother with three kids who one day realizes she’s not sure how long there have been four babies in her house, and even though one is three times the size of the others and looks very different, they all have similar lower faces so she can’t really tell and feeds them all just to be safe.