I realized that I was looking at the wrong Sounds options. The Sounds I was looking at was just showing you what was set for that theme you had selected. A simple trip to the Sounds applet in Control Panel solved my issue. Thanks for the help!
Thank you for that link! Unfortunately, my Sounds window looks similar but I cannot see anyplace where I can change what sound plays, or turn sounds on and off. It just shows me the list of events which can trigger sounds, which ones currently do trigger sounds, and what sounds they trigger (as well as the file location of said sound).
I'd consider just deleting the sound or replacing it with an silent file, but that would be a little silly IMO.