We've discussed this before-- remember where, mods? So there's more speculation on this if you can find it.
Anyway, from what I can tell, George started out quite chatty (look for 1963 YouTube clips), but gradually clammed up out of sheer boredom of answering the same questions again and again. By the time they'd reached America, the first buzz had worn off and George only spoke up when he cared to. You can still see him animated on occasion, but between Paul's willingness to answer anything, and John's wisecracks, he often didn't bother to say anything, so the American press invented this label to distinguish him from the others.
He wasn't quiet in person. Who said the quote "None of them are particularly quiet." I think it was Linda who reported coming to a Beatles dinner, and it sounded like there were 100 people in the house when there were, like, 6. I love Michael Palin's remark about George in the Concert for George
extras: "He could talk for England."
Larry Kane has a lovely chapter in his book "Ticket to Ride" where he gives his impression of each Beatle. Here's a quote specifically pertaining to George and his quietness:
George was always the most polite Beatle, but it seemed to me during this 1965 tour that George had suddenly blossomed into a more public figure. On the way to Houston, I sat down and recorded a relaxed George Harrison.
KANE: On your first US visit, George, you were known as the quiet Beatle, the somber, thoughtful and pensive one, and suddenly here in 1965 you've kind of, according to most people's way of thinking, opened up. You're talking a lot at the press conferences, a lot of the questions are directed at you. What's the reason for all of that?
HARRISON: Actually, I did talk about the same amount on the last tour. It's just that, you know, first of all, when we first came over here they didn't know us all that well. People, like, hang tags on you. Ringo was the cuddly one or something. Paul was the lovely one, and I was the quiet one, and John was the shouting one. I've been the same all along. I talk when I feel like it. I shut up when I don't feel like talking.
That last line tells you all you need to know about George Harrison: no pretense, no showboating, a strong sense of self and, for an entertainer in the glare of the spotlight, nary an ounce of superficiality. But he definitely was, on the second go-round of America, less shy and more willing to speak out.