I had 4 interviews where I needed to be exceedingly clever very quickly. I was for two of them, and wasn't for two of them, and so I was a no-hire. Given a few days to think through the problems again, I was able to solve them all in my head- just not in 45 minutes. None of the interviews asked about my ability to design systems, how to test or manage large-scale applications, how to gather requirements and work with customers.
My conclusion is that Google is primarily looking for people who either have every algorithm and problem memorized and ready to regurgitate, or exceedingly clever people who can solve tricky problems on the spot. I guess this works for them, as they're a very valuable company. On the other hand, I sometimes wonder if it works despite this process they have.