Anecdotally, at a previous company, we tried an "open book" (i.e. you can use the web) interview policy for a few interviews. It was a train wreck.
Google's insistence on this preparation thing is doubly weird to me when I consider that literally nobody "prepares" for work every day in this manner; knowing what a developer can do after studying his brains out regarding things that will be ejected from the brain again immediately after the interview doesn't really send a meaningful signal.
Begs the question, doesn't it?
>> Binary trees are MOST ASSUREDLY on that list
Sure they are... and my intro to CS textbook was ~500 pages. I'll bet I could find something to trip up just about anybody, especially when coupled with the pressure of doing it in front of the class ^H^H^H people that have $$$$/power over you.
I prefer not to ask code questions at all, though.
If all someone needs is help remembering the name of a specific function, then I'd rather provide them with that if I remember it or just spot them it as something trivially Googleable. I wouldn't hold that against someone unless it seems like they're completely unfamiliar with the language they've chosen to use. There's no need to give an otherwise good candidate the chance to self-destruct over trivial details like that by obsessively Googling everything to make sure it's exactly correct when that's not what I care about, and in so doing they aren't paying as much attention to overall algorithmic details, which I do care about. If they need more help than trivial Googling, then they can't solve the problem anyway, and me watching them thresh around on the Internet isn't helpful to anyone.
A good analogy is laptops in classrooms. A lot of students will attempt to use laptops to take notes, even though they inevitably serve as a distraction, and study after study has confirmed that students actually learn better when they take handwritten notes. Somewhat paradoxically, studies of classes where professors have banned laptops and forced handwritten notes show higher student happiness; they're aware on some level that they're more engaged with the class and are learning better, and appreciate that the choice to distract themselves is removed, because if the choice were possible, they might not be able to exist. Well, providing someone access to Google in a coding interview is very similar to letting students use laptops in classes, in a lot of ways.