Hey Stephane,
This is something that freaks a lot of people out…
What we call an Object in 3D, is a Coordinate System (with a per Object name).
Where (for instance) the Vertices of that Object are in it’s Coordinate System, are stored in a list (‘Mesh Data’).
If you Scale or Rotate or Translate a Cube in Object Mode, the Coordinate System gets Scaled or Rotated or Moved, but the Vertices’ Position stays the same:

Linking Object Data, means, that you can change the Position, Scale and Rotation of the linked Object’s Coordinate System, but the Vertices’ Position doesn’t change.
This is something a lot of people struggle with.