I don't think they necessarily "corrected a few mistakes without giving them back to the mob". There is also a chance that they indeed proposed their answers to

I don't think they necessarily "corrected a few mistakes without giving them back to the mob". There is also a chance that they indeed proposed their answers to the mob, but they didn't like them and rejected them. It wouldn't be the first time that a great idea is shot down because it's too far from everyone's comfort zone. But I'm just guessing.