Thank you all for your insightful comments. I do feel a little better and more informed. I will try to write an unofficial summary using what others (mostly the official wordings from Googlers (sigh)) have said, mainly for people in the same boat as me.
1. You don't have to be from an Ivy League university to get recruited by them. Yay.
2. Internal references are very very important for both getting recruited and getting feedback after the interview.
3. Getting recruited by Google can be very very competitive at times (not necessarily always), and you can be unlucky enough to be interviewing in those times.
4. There is no easy solution to the shallow feedback problem, which sucks very much for the candidate, but I guess threads like this can help you get some insight into the process and the very many variables involved in the recruitment decision.
If you want feedback, ask a smart friend (or a professional service) to mock interview you and give detailed feedback. That's better than what any official employer could do.
1. You don't have to be from an Ivy League university to get recruited by them. Yay.
2. Internal references are very very important for both getting recruited and getting feedback after the interview.
3. Getting recruited by Google can be very very competitive at times (not necessarily always), and you can be unlucky enough to be interviewing in those times.
4. There is no easy solution to the shallow feedback problem, which sucks very much for the candidate, but I guess threads like this can help you get some insight into the process and the very many variables involved in the recruitment decision.