It seems to me that the buttons are: main textual flow of a document."
"...content that is tangentially related to the content that forms the main textual flow of a document."main textual flow of a document."
Am I right in thinking this?
My opinion, those buttons are a great use of the aside tag. They are content related to the main content, but completely separate entities. Actions to take on the content, aside from the content itself.
Asides I see as just things that are related. They are related to the entry, but not about the entry directly. Basically, they add context/extra instead of content. A personally story about disneyland may have an aside describing what disneyland is, or where, or other information not about the story, but helping explain things more. I would personally file actions on the story as an aside because they are not adding content to the item, but expanding upon it further with extra information (in this case, sharing it with others).