My experience was similar to yours. I interviewed at YouTube, and I was flown over from New Zealand for the interview. When I returned the next day, I got my generic rejection letter with Dear {Full Name}. While I got the general solutions to the 5 questions throughout the day correct; I struggled to code them on a whiteboard with someone watching me; I can never think well in those situations when solving problems, but I find that the optimal solution clicks to me when I'm in the shower or wake up in the middle of the night.
It would be good to get some feedback about how to improve and where you went wrong. It's pretty hard dealing with a generic rejection after flying for 14 hours to the other side of the world for an interview! If the rejection is because of technical skill, then I think they could figure that out from a few more phone interviews (although I guess a free trip to the US isn't too bad).
I don't think it's because of the university though. One of my friends from NZ got a job out there and he was from my university, which doesn't have a particularly high reputation for computer science. I think he just knew how to nail the technical questions under pressure, and is more interested in algorithms and low level stuff than me, perhaps.