It means a lens can only be precisely focused at one subject distance at a time. Objects at that distance form the sharpest image on the film or sensor, while objects slightly nearer or farther may still look acceptably sharp within a limited zone called depth of field.

So the statement is mainly about focus and depth of field, not about the camera body having a small amount of lens movement. A focusing mechanism is needed so you can choose which distance will be sharpest.

Your thin-lens formula is relevant to how focus is achieved: changing the lens-to-film/sensor spacing changes the subject distance that is in focus. But the quoted sentence is not specifically saying that the camera has a limited focusing range. It is saying that, because of how lenses form images, not everything at all distances will be perfectly sharp at once.