Having an accept rate slightly less than 100% is not the end of the world. My accept rate on Meta is 88%. Jon Skeets accept rate is a miserable 95%. It's when your accept rate becomes low and red then people start paying attention to it and you should take action to increase it (asking more answerable questions or actually ticking the green box next to valid answers).
It's your responsibility as a question asker to get your question answered; whether you do that by pestering the author of the wrong answer to update it, offering bounties to get more attention for the question, or adding an answer yourself is up to you.
I applaud you for doing this by-the-book though, and not just accepting the wrong answer to keep your 100% accept rate.