When is the last time you heard of a system administrator writing down problems on a whiteboard as opposed to asking a colleague or Googling the answer? I think the real test after the initial phone call interviews and Google docs one is to sit you down in-front of a computer and make you solve real problems, not theoretical & made-up problems in which they ask you to solve them in impracticable and unrealistic ways.
This is a flaw in the corporate hiring process almost everywhere in the software world. It's not the 70's any more, people rarely solve problems on whiteboards and paper. They solve them on the computer, sometimes through knowledge and their skill-set and other times through luck and Googling.
Don't feel too bad for being rejected, it just means something else could come along that's better.