Kleppner refers to the displacement vector as a 'true vector' in the sense that while it's coordinate values depends on the initial and final points in a coordinate system, the vector itself does not.
What specifically does this mean? Is it merely a physics way of referring to a free vector?
Yes. The displacement vector from (2, 1) to (5, 7) is the "true vector" or "free vector" <5- 2, 7- 1>= <3, 6>.