I am hiring engineers (systems, software and security) in the last 5 years, got trained up on recruiting by Amazon, so I would say I have a pretty good understanding on hiring.
The right approach with these interviews to find out the best of the candidate. In order to achieve that you always start with simple questions like what is a variable, what sort of data is out there, do you use version control etc. After that you switch gears.
On the subject of inverting binary trees on a whiteboard. Is this the core of your business? How many times did you need to do that last week? If it is irrelevant for your daily operations than why are you asking this question?
The problem is that (especially companies like Google) like to hire Stanford graduates and those guys think after being in the job for few months that the best way on interviewing is to measure how well the candidate would have done during the last semester in theoretical CS class at the university. While we probably all know that running a service for millions of users in production in a distributed environment requires many other skills that are not represented too much in the interviews, yet this is what you can run into during the interview loops.
I think at certain extent this is known to the Google recruiting team and they are ok with it. The way to beat the interview is to read books like Cracking the Coding Interview and train up extremely well on those trees and search algos and all, if you are really committed to work there. There are several very senior guys turned down by Google simple because they failed one or two of these ridiculous questions.
I think the last incident kind of a good example of this:
https://twitter.com/mxcl/status/608682016205344768
Now I get back to my read about how the heck I am inverting a binary tree.