Yeah, I read an article about this. Some people think any cut hurts the tree, but removing dead branches is like basic first aid. It stops diseases from spreading and keeps heavy dead limbs from falling on someone's house. That neighbor probably just doesn't know how tree care actually works.
Guess they'd rather let the dead branch fall through their roof. Hernandez.brooke has it right, it's just basic tree first aid. Some folks just enjoy being wrong with confidence.