Of the four, George was by far the least impressed by fame. It should come as no revelation to anyone reading this that he outgrew being a fab far quicker than the other three. Even into their forties, John and Paul still worshipped Chuck Berry and Little Richard just as much as they had done in their teens, whilst George went on record as saying he'd never REALLY been bowled over by anyone until he met Ravi Shankar. It's like being in The Beatles was just a stepping stone for George onto highier and mightier things... remember that famous quote about joining The Beatles being the best professional move he ever made, but leaving them being the next best? Despite being the youngest, I also feel he was the deepest and the one who grew fastest and furthest, if that makes sense. I don't hold any of this against him in the slightest.
Of the many things I love about George, his avoidance of becoming starstruck was one of them. He didn't court fame ("I said I wanted to be successful, I never said I wanted to be famous"). Sure, he fully embraced the perks that stardom and global adulation sent his way but, despite his love of fast cars and palatial houses, he was the first to grasp the transient, ephemeral nature of these comforting things. They were toys, pleasant side effects. He wasn't so much impressed at being a star as semi-comfortable with it. Certainly he WAS proud of being a Beatle and would occasionally display it... it was he who suggested and encouraged the Cirque du Soleil "LOVE" concept celebrating their catalogue, for example.
For all John's reputation for uncompromising honesty, I've always felt George was the "least false" Beatle, if that makes sense. He was the least comfortable at putting on a showbusiness mask and "playing the game" whereas Ringo lives and breathes "showbiz" and Paul, much as I love him, is a positive "ham" at times. They feed off an audience; George just wasn't wired up the same way - he didn't mind doing the odd gig but the thought of a tour horrified him. Far from making him ungrateful or aloof I think it highlighted his mystique and, at the same time, his honesty. And yes, he could undoubtedly be saturnine and even downright gloomy (occasionally) but that droll, sardonic humour helped to balance out Ringo's goofy fun, John's near-the-knuckle cheekiness and Paul's undimmable, optimistic zest.
As for Harrison's input on Pepper: hiding behind an alter ego was the furthest thing from truth-seeking George's mindset at that time ("Nelson Wilbury" was still more than twenty years away) and one profound track would mean more to him than three catchy standard ones. It's not as if he didn't try: even post-Pepper, he alone from the group visited Haight-Ashbury but saw through the hippy hype. He was simply distracted by other, more meaningful (to him) things.