This is a difficult error message to diagnose, mainly because it doesn't give you any useful information about the real error.
Can you PLEASE add more debugging info into wp_ajax_upload_attachment() in ajax-actions.php to improve actions such as:
if ( ! current_user_can( 'edit_post', $post_id ) )
outputting some json message before dying would greatly help anyone who encounters the upload message - because most of the advice given to resolve this error is of little help
In this case, when logged in as the administrator, I don't have permission to edit posts (strange?!). and so cannot upload images