Anyone with access to your private Brandboards can comment on those pages. This includes collaborators, as well as people you invite to view-only.
Comments are hidden from public viewers of public Brandboards.
As the owner of the page, you will be able to delete any comments that you don't want included on your page. The people who write comments can also remove their own comments at any time.
Collaborators can also use the Discussion tab to comment on your Brandboard.