I have read the following threads:
Scripts cannot be accessed or run at all by anonymous users, unless they are deployed as a Web App, and even then only the front end is accessible by an anonymous user.
You'll see in your bound script that users who are not logged in cannot even access the script editor by clicking tools -> Script Editor (But all logged in users can). Additionally, if you have a standalone script in your Drive, and you right click and share to 'Anyone on the web can edit', anonymous users are still required to login.