The folder “iTunes” is on a locked disk or you do not have write permissions for this folder.

I've already right-clicked on the application, clicked "get info", and changed it so all people listed in the "Sharing & Permissions" section have the "read & write" privilage.

The error message is referring to your iTunes library, not your iTunes application.

You need to check and fix the permissions of the iTunes folder in your iTunes library. This is by default located in your "Music" folder.

Select the folder Music > iTunes in the Finder, right click on it or Ctrl Click and click "Get Info". At the bottom of the contextual window thatwill pop up, disclose the Sharing and Permissions brick, change your status from Read only to Read & Write. You may need to click the padlock icon to make changes.