This comment raised a question for me
During the Chamber of Secrets while Harry is in Riddle's memory he is described as gliding alongside Riddle, watching whatever Riddle saw (however this not really being the pensieve, riddle might be explicitly directing what Harry could see)
Again, when Harry is in Snape's memory in Order of the Phoenix, it is described that Harry hoped Snape would go out of the exam hall in such a way that his parent's would stay in view, so that he could watch them, because otherwise if Snape went in the wrong direction, he would not see his parent's in the memory either
But then again, in the answer linked in that comment, although the memory is from hokey, when she leaves the room, Harry and Dumbledore do not glide out of the room with her, but instead stay in there and see and hear the events that happened between Riddle and Hepzibah Smith
What is the extent of the pensieve's power for showing the world not seen by the original owner of the memory?