At the moment it is not possible to grant OAuth consumers the right to edit captions. For example, calling action=wbsetlabel&language=en&id=M123&value=Blah results in "You do not have the permissions needed to carry out this action." even though the authenticated user has the editpage grant and is able to edit the page content.
Customize query in gerrit
|mediawiki/extensions/WikibaseMediaInfo||master||+5 -0||Add the mediainfo-term right to the editpage grant|
This is now working (on beta Commons anyway).