The phrase "The Latin Mass" is usually reserved for the traditional Catholic Mass of all time (until Vatican II). Ocassionally it is used to refer to the New Mass done in Latin, which is really a mis-use of the term. In this instance it is clear that Bishop Olmstead is referring to the traditional Latin Mass, and not the New Mass said in the Latin language, since he mentions Pope John Paul II's indult. The traditional Latin Mass is always said facing God. I have seen the New Mass done in Latin both facing the people and also done ad orientem.
The truth of the matter is that Vatican II is only now beginning to take effect, just as the Council of Trent took several genarations to take full effect.
For the Latin Rite of the Catholic Church, Latin is the official language. The Order of the Mass promulgated by Pope Paul VI, what others have "nicknamed" the Novus Ordo (not it's official title), can always be said in Latin. In fact, Latin is the normative language. Priests need permission from their Bishops to say this Mass in the venacular language (for America, English), not the other way around. It was never the intention of Vatican II to banish Latin, quite the opposite.
Of course, practically speaking, with a universal indult here in America as well as other countries for the venacular language, the vast majority of Masses are said in the venacular. Additionally, despite the fact that Priests of the Latin Rite are supposed to know Latin, many do not. This excaberates the problem. For English speakers this fact has been especially horrendous due to the incompetent, agenda driven translations that have been used up to this point. This fact is in the process of changing. It will take time.
The indult Mass being talked about here concerns the "Tridentine" Mass as of (I believe) 1962. The Pope allowed an indult for this version of the Mass to be said in the 1980's with the desire that it be widely available for those who wished to worship liturgically with it. Similar to the "Novus Ordo", it has never offically been translated into any venacular so it is obviously said in Latin.
An indult means permission, for at least a certain time (if not more), to lawfully do something not "normative" in the Church. For the Tridentine Mass, it requires among other things, that the individuals participating fully accept the Vatican II Council. It also requires permission from the local Ordinary. That had been the sticking point in Phoenix up til now. It indeed is the sticking point for many Dioceses in this country, as fellow Freepers can and do testify. I can only urge them to patience. Schism is never a valid answer.
Regarding which way the Priest faces, I always understood that the universal rubrics for the "Novus Ordo" actually assumed the ad orientum position of the Priest for the Eucharistic Prayer. The Bishops in America may have requested and gained adapted rubrics for our country favoring the ad populum direction. I'm not clear on that. In any event, either direction is valid. And this, for both Masses. Consider St. Peter's Basilica in Rome and the Tridentine Mass being said there. Actually, the Pope could do both ad orientum and ad populum at one and the same time!
A generation of shoddy catechesis and poorly formed Priests, engineered by a cabal of dissidents trying to mastermind a mid-level takeover of the Church under guise of "post counciliar reform" has caused tremendous harm. The take-over has cracked and is sliding backwards as a new generation comes up to clean up the mess. The 2,000 years of Church history has seen this story played out before.