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Authenticated users do not have access to edit media files in gallery even if their are authors of that gallery and files.
Of course I check all permissions correctly (edit own files etc.) and I track down that problem is in media_gallery_filter_media_access function file_entity_access always return NULL. So it can be problem with file entity (I use 2.x dev) but not sure.
For me was enough simple hack/fix with let authors edit his files but this need more deep track why could not use normally multiedit.