So, having said that: the Tome of Damasus anathematizes all of those who reject the Trinity. The Council of Ephesus condemns all of those who reject the Nicene Creed.
Muslims reject the Nicene Creed and the Trinity. (They consider it blasphemous, in fact.)
Therefore, for the Vatican Council to assert that "Muslims worship the same god as Catholics," meaning "the same god in all his attributes and in every respect," not merely "they got some of the basics right" -- then they would be anathematizing themselves.
That is impossible (and of course there was no change in Catholic belief regarding the godhead at Vatican II), hence the premise -- that VC II asserted that Muslims worship the same god as Catholics in all his attributes and in every respect -- must be false.
I disagree with the above ascertation.