Haycox uses the term "ownership" and its cognates in three different senses, without differentiating among them.  So he compares oranges to apples to bananas and comes up with the fruity conclusion that the Tlingit lost "their" land with the Purchase.  

Aboriginal title did not imply possession of the land: Native Americans did not think any man had power to fix limits to the environment and were puzzled at the European belief that this was the only "civilized" way to live.  Imperial title was chiefly a matter of conquest, exploitation of the Native people, and defense of commercial interests against European encroachers.  Common-law title is what we are familiar with, and it is the sense that Haycox anachronistically projects backward to the situation in 1795, and then in 1867.  It's not possible to "give back" the Tlingit land in the common-law sense, for the aboriginal Tlingit themselves never defined it that way.