The Engineer was only after Weyland and David, no one else had to die.

The Engineer was waiting for some sign of respect. David and Weyland, showed no humility whatsoever, so they had to die. Think about it, the Engineer was perfectly calm when he came out of cryosleep, he just stared. Then Weyland signals himself as the leader of the group in a violent way, by indirectly hurting Shaw. David makes it worst when he blabs out his dying master's unreasonable request without so much as a 'hello' or 'how do you do'. (whatever David said was VERY BRIEF, and sounded more like an order then a request.) After the Engineer gives David a "WTF did you ask me, you cheeky bastard" look, he caresses David's head and realizes that David is an A.I. so he tears David's off and uses it to kill- not the security, not the doctors- but Weyland, the leader, the most pitiful looking, physically week, person in the room. The Engineer was trying to establish himself as the Alpha Male. But then the bodyguard shot him and it all went to hell from there. Had they done things Shaw's way, they might have avoided unnecessary death. The Engineers are not unreasonable people. Shaw knows this and probably knows how to address them and what to expect. She's an History buff for crying out loud, and perhaps knows some things David doesn't, like more about the Engineer's history on earth, like more obscure mythology behind them. Otherwise, she wouldn't attempt going to the Engineer's homeworld... unless she's completely lost her mind.