Your daughter is in fight or flight mode. Her nervous system is in control of her, not the rational part of her brain. She's telling you she's afraid and even if she's lying and being over dramatic I'd have the same suggestion.
She also knows the behaviour isn't ok, so it's not suddenly that she's become an uncontrollable child in all areas (from what you've said).
Also we want to teach our children to listen to their instincts. We don't want them to learn that they need to prioritise someone else's feelings over their own instincts. Particularly with women, that doesn't lead anywhere good.
So, acknowledge her fear. Tell her you understand it. You don't feel the same way but you understand that for little girls, old ladies can be scary sometimes. Promise her she's not a witch because you're and her DF would never live near a witch. Tell her you're there for her and want her to trust you (give some examples of things you do that she likes) and say that you want her to hold your hand when you pass the NDN and squeeze it if she feels scared. Tell her she can squeeze as hard as she can if she needs. And then do a few practice squeeze at home. Also tell her that you don't want her running off screaming but you do want her to feel safe - and the safest place is with you. Have her walk on the opposite side of you to the neighbour and to start with don't ask her to wave or smile, just stay with you. Later add in the other bits (or she'll get over it and go back to normal anyway!).
When I was about the same age I became utterly petrified of some old women who looked like witches to me. I can still remember the terror. I was also petrified of an elderly man who drove me to school. He did nothing wrong, I just found his glasses (brownish lenses) and the lines on his face very scary.
So a sort of adult version of this situation would be you seeing a gang with knives walking towards you down the street, you running inside in a panic. Once inside the door, you're berated for not waving at them and smiling politely and then in trouble for it! You'd probably not respond with the most polite version of yourself either!
Speak to NDN and telling her DD is going through a phase at the moment and tell her it's not just with her if that helps. She's an elderly woman, she's lived a long time and not some kind of fragile flower. I'm sure she understands children go through phases etc.