I know it's an accident, but I think the show often makes a good case for keeping Laurel in the dark. I mean, even in this ep, when she was getting angry at Oliver, she talked about him being the Arrow in the middle of the hospital hallway. If someone let slip that Quentin was working for DD (especially if she found out that Quentin kept at it because he threatened her), she'd go right to him and confront him, without even stopping to consider that maybe he was double-agenting. So Laurel!