The difficulty lies with the next phrase of Article VII of the Confession of Augsburg (you have paraphrased the first part very well) "and the Sacraments admnistered rightly".
What constitutes "right administration?". And how is the ordering of ministry connected with such right and proper administration?
The uproar over the Lutheran-Episcopal "Called to Common Mission" agreement (an uproar which has not subsided) is precisely over that point: Is connection with the historic episcopate (which may or may not be the same thing as Apostolic succession, depending on one's point of view) a necessity in order to administer the Sacraments rightly and in a manner consistent with being the True Church?