The other thing is that these interviews almost always enforce no Internet access. If I was in a position to hire, I'm looking for people who can solve problems, not those who can remember the Java API in their head. If their first instinct is to open Javadoc, then my reaction should be "good, they know where to look for to make sure it's correct" not "God, why can't they just do this [arbitrary task]?"
I'm hoping to finish my PhD and become a professor in Computer Science. My plan, given university constraints, is to never once offer a written final. I've not once taken an exam where I was confident just writing code down. It doesn't make sense. Offer them a final on a computer with Internet access, but with a sufficiently difficult problem that it can't just be Googled for a complete answer. Their web access logs are turned in with their exam, so I can see if they copied something if it looks suspect, or if they're borderline I can give extra credit for going through a mental process that shows promise.