I think people are overreacting to the Prince Andrew thing. That's his daughter. I can see why people why people would feel it is inappropriate regardless of what we know about him. However, sometimes moments captured on camera can look worse than how they are in reality. Do people really think he's going to feel up his own daughter in front of the worlds cameras?
What's more likely is that he's tried to keep hold of her, comforting her while he bends down and has not realised whats happening as he's doing so.