That is true.
The other case in point is more frequent. For the purposes of this example, let's say that person A makes the request. Suppose A publishes information on a social network and that B, a friend of A's, then shares the information about A more broadly. This is where B's freedom of expression is at play, and that is where we have to find a balance between A's right to protect his reputation, and what we must take into account to remove information; is the information accurate, complete and up to date, and how is public interest served, if it is involved at all?