Are large tree branches hanging over a house a recipe for disaster?

People around here get trees cut down to stumps rather than risk having a branch fall on their house. But is it not true that branches, especially in non-snow climates, can hang over a house for decades and stay there? A great example:

https://scontent-atl3-1.xx.fbcdn.net/v/t1.0-9/12140741_10205953344464700_1373717981358435593_n.jpg?oh=df39b25d0983b5c8d494487c0581ec33&oe=580B68A3