The story of the Tree That Owns Itself is widely known and is almost always presented as fact. Only one person—the anonymous author of "Deeded to Itself"—has ever claimed to have seen Jackson's deed to the tree. Most writers acknowledge that the deed is lost or no longer exists—if in fact it ever did exist. Such a deed would have no legal effect. Under common law, the recipient of a piece of property must have the legal capacity to receive it, and the property must be delivered to—and accepted by—the recipient.[6] Both are impossible for a tree to do, as it isn't a legal person.

[...]

"However defective this title may be in law, the public recognized it."[11] In that spirit, it is the stated position of the Athens-Clarke County Unified Government that the tree, in spite of the law, does indeed own itself.[12] It is the policy of the city of Athens to maintain it as a public street tree.[13]

[...]

Although the story of the Tree That Owns Itself is more legend than history, the tree has become, along with the University Arch and the Double-Barreled Cannon, one of the most recognized and well-loved symbols of Athens.

https://en.wikipedia.org/wiki/Tree_That_Owns_Itself

In reality, the tree is not protected by law, but by the will of the people. Kind of symbolic if you ask me.