Why would she need to show off? She already knows she's better than him. ;)
In all seriousness though, it just makes sense that if Edwin got killed, she was the reason for it. They were left alone in the common room, so they could have got to talking and he let something slip that he didn't think would catch him up, except she caught it and realized he was really working against Hawk, so she took care of it. She wouldn't feel the need to brag about it, and so would create a story that had him leaving in good health the night before. It also wouldn't matter if anyone believed her (though hawk would know the truth, of course), because they'd have no evidence to back anything up one way or another.