I'd settle for the interviewee understanding big-Oh notation and being able to explain the complexity of an algorithm, given an implementation in a language they understand. If they can do that, it means they have the skill you're really looking for: that they can detect an unnecessarily expensive algorithm. (Isn't that really what the sorting algorithm questions are all about anyway?)
They don't tell you why they approve/reject, but I imagine that they probably have a similar process on the other side if you are hired with regards to the package you're offered. Very likely, they'll seek to optimize the right amount to give you.
And yes, I do think they're probably missing out some great talent, because not everyone can scribble it out on a white board on-the-spot. But you have to be able to communicate effectively to get anywhere, even in Google.
I'm interested in seeing whether the same mix of staff and company structure can prosper in a recession.
What's fundamental is that it is those few abnormal people who change the world 1000x more than the regular person. When you have near infinite money like Google, I'd be very afraid of missing out on those few people who are going to carry the company.
Google's strength was that meandering "lets just work on what seems coolest" ethos. I'm wondering if they're not selecting out some really great talent by making the interview a test of how well a candidate can scribble some common design patterns on a white board.
I'm not saying that they should hire programmers that can't tell a merge sort from a bubble sort, but perhaps just knowing the difference and when to use them might be enough; Rather than finding out if they can write it out syntax-perfect on the spot in the interviewers favorite language.