O Fortuna would be considered a "common phrase" and is not eligible for copyright protection. So whether or not is it "public domain" is a moot point. It may, however, be registered as a trademark....
In terms of intellectual property "public domain" refers to items that have no restrictions of use due to expiration of legal controls (patents, trademarks, copyright)
Pubic domain occurs naturally when a copyright expires. In theory, a copyright owner can intentionally disclaim any power to enforce a copyright, making it as if it were "public domain".
There are only two Mr Ed episodes that I've been able to confirm that are in the public domain. ""The Wonderful World of Wilbur Pope" and "Wilbur Gets the Message... About Savings Bonds". However...