I wonder if Kurt really said that about Keanu? (not that it really matters, his character judgement isn't the standard I hold for people. Just cause Kurt says it doesn't make me believe it) Keanu and River were very much alike, it was said by people who knew them both, including Gus Van Sant and Sandra Bullock. River said Keanu was like his older brother, if he was such a faker I highly doubt that River would bother saying that. Plus both of them were known for not really hanging out with the other "young hollywood crowd" at that time.
Keanu is also very down to earth, more so than Depp IMO, who has really pushed this image of himself out there, and despite popular opinion, seems really affected to me. For not caring about the Hollywood image Depp sure does mention it quite a bit. KR always kept his head down and worked. He has never paraded his girlfriends around in photoshoots or needed to prove how bothered he is by fame by buying a private island, and then claiming to do so in order "feel normal". Despite his megastar fame he still moved through the world and stayed simple in comparison to his peers (owning a moderate house by Hollywood standards and still driving a 13 year old car). He's never pretentious and doesn't act above it all. He stays true to his word when he says he wants to keep his private life private and that's that. He doesn't make a big deal about it. I feel like he doesn't get enough credit, ironically enough, because he is so successful at shutting down the press that he has really managed to stay out of the limelight.