I've had two rounds of interviews at Google and I would not characterize a single one of the individual interviews I experienced as requiring "random knowledge" or "quick answers to logic problems".
I think there is a real danger here of extrapolating the experiences of one or a few people to a statement on hundreds or thousands of interviews/interviewers. At the rate Google is interviewing candidates it should be expected that some interviewers are not good interviewers.
After doing a lot of research on the subject (to prepare for my own experience) I can say with some certainty that based on reports from people that actually went through the experience, interviewers asking for brainteasers or "random knowledge" are in the clear minority.
(At least for software engineering interviewing. The questions for product managers seem to be a whole other beast.)