I mean I guess I fail to understand why if you show that you know the algorithms you are trying to implement, and the data structures needed to do so, what does it matter if you rely heavily on auto complete to give you the correct method calls off of those objects when programming?
I realize a programmer using auto-complete which knows the method signatures well enough to not use auto-complete, will have a slight speed advantage while developing over someone who actually needs auto-complete. But there have to be better ways to test for development speed if that is truly your concern.
Similarly I realize the interviewer would like to see how you respond when you can't remember or don't know something, do you get frazzled and frustrated or do you ask questions. However there are definitely far situations you can create to to watch for these type of reactions than simply expecting someone to know the syntax of a language well enough to write it on a white board.
Honestly what am I missing?