Can an image on a screen really invoke such an emotional response?
Of course it can. They are designed, engineered, and created (by people who makes LOTS of money) to do exactly that. And when it works out right, it is art.
I can cry (or at least tear up) for any of the following, at almost any time.
- Bogart's speech to Bergman in Casablanca, when he says "We'll always have Paris..." Timeless
- Carlos Santana playing Samba Pa Ti, or Jerry playing and singing Stella Blue
- The end of It's a Wonderful Life
- Standing in front of The Sleeping Gypsy by Henri Rousseau at the The Art Institute of Chicago Museum.
Or try any of these: Terms of Endearment, Beaches, Night and Fog, Schindler's List, E.T.,
So yeah, they invoke emotions, they are supposed to. There are several scenes in LotR that do it for me, the one you noted when she says "I am no man" or the incredible love story between Samwise and Frodo, which is the heart of the book, and the best part of the adaptation. You feel it, because these people are good, and they are all doing good work, and that's what they do.
Emotion is the name of the game, in rock music, and perhaps in all music - listen to Dylan sing The Lonesome Ballad of Hattie Carrol, or Beethoven's Ninth - the sound, fury its so uplifting its almost a drug. Movies (and remember laughter is just as emotional as tearing up), greeting cards, commercials, especially holiday commercials, have as their stock and trade emotional manipulation (hopefully in a good way - though watch Leni Riefenstahl's Triumph of the Will for the bad way).