For whatever reason I'm having trouble opening the official Vatican web site, but I'll keep trying until I log off (I'll be offline for the next two days for the holiday). However, if I can't get there to post the link just go to the English language page, then to "Scripture" or "Bible," then to "Pentateuch." They don't use the words "documentary hypothesis," but they teach it (they claim that the Torah/Pentateuch was compiled centuries after Moses by various "schools of thought" and thus late date it by centuries). Look for references to "J, E, P, and D." That is the essence of the classical theory.
What you're reading is the foreward to the New American Bible, which is the default American English-language Catholic translation. It wasn't produced by the Vatican, it's just on their website as a resource. (I believe it was produced, indirectly, by the American bishops.)
The notes, in terms of authority, are about at the same level as most any Catholic book you'd pick up at a bookstore ... that is, it has the nihil obstat and the imprimatur, meaning that a bishop and his censor approved it, but it's hardly infallible teaching binding on the faithful, nor is it even at the level of something a Vatican congregation would promulgate.
Catholics are free to deny the documentary hypothesis. Here: watch me. I'm Catholic, and I think both the DH and the similar "Q" theory of the Gospels are historically bogus.
Go ahead: write a letter to my bishop denouncing me as a heretic. ;-)