I was talking to someone about the new LinkedIn View Profile feature, and they were concerned about people knowing exactly who was looking at their Profile.

Fear not; like most of LinkedIn's features, there are visibility options.  Remember, this is an opt-in and mutual acceptance site. 

If you haven't already done so, I strongly suggest you go into your settings and see exactly how you can play around with them (the way to get to all of them is top of the screen, right side, Account & Settings).  For the visibility, they can't make it any simpler:

Profile Views