I think that one of the problems resides in this bussiness of drawing lines of faithfulness between movies and books in the first place. Cinema is a different media from literature.
Not to talk of rendering an epos like LotR into a different media. You're never going to accomplish that and thence dicussing about faithfulness isn't exactly to the point?
But that does not mean that the value-meters you Sauron brought forwards are any good either. There are reasons (a lot of them) to say PJ's movies were beautiful to look at but shallow. But these reasons need not tie themselves to the "faithfulness" aspect.
They were shallow as cinema.
The box-office ratings? Quite a many people went to see "The Independence Day" as well... Remember, most people go to see a movie once so they have not known what crap it was but the marketing hype was loud enough to lure them into the theaters. I'd believe more any "after-movie polls" than just pure attendance numbers. And anyhow quality and quantity are different things after all?
Collective praise by the critics? I'm not sure about the U.S. if every critic is fed by the big movie-corporations but at least in Europe I think most of the critics had a long list of reservations and some even scorned the whole project. So at least here it was not a "collective praise"...
The industry awards? Well what else could they have done after the popular phenomena the movies made? What would have been the Oscar-committee's credibility rate after the third box-office hit? If they'd given the Oscars for a good film they'd at least picked the first one but for some reason they didn't...
But to be serious... that was an after-award as ever there was one! They couldn't just not notice them at that point.
But coming back to my basic idea. As film and literature are two different medias both should try to excel in those areas their media makes them excel.
PJ probably tried his hardest (at least in some part) but just couldn't make it.
So a brave interpretation would have been in place, original view with an excellence in telling the story via a film-media, and hopefully lots of money behind to make it look good as well... PJ's was a compromise with some highly potential visual & musical artistic aspirations blended with box-office requirements (the storyline, the cast...) - and possibly PJ's shortcomings as a director...
Sorry to say this. I loved the films for what they looked like and I love the music as well... but as movies... no I can't love them as movies.
EDIT: Looking backwards into the thread this clearly is steering far away from the actual topic... I'll promise to try and stay better in the topic the next time.