Ahh... it's freaking Download Deputy (which I deleted a month ago). Apparently the uninstaller doesn't remove the plugin, so when it tries to download and can't find the application, it goes to Script Editor for some reason. VersionTracker reviews for that piece of garbage are full of people complaining about the same thing.
The moral is, don't install Download Deputy. Use Speed Download instead. Thanks for the help, Krusty...