Insulating CuF2 is considered a prototype compound displaying a Jahn-Teller effect (JTE) which gives rise to elongated CuF64- units. By means of first-principles calculations together with an analysis of experimental data of both CuF2 and Cu2+-doped ZnF2, we demonstrate that such an idea is not correct. For ZnF2:Cu2+, we find that CuF64- units are compressed always along the Z local axis with a hole essentially in a 3z(2)-r(2) antibonding orbital, in agreement with experimental EPR data that already underline the absence of a JTE. The structure of the monoclinic CuF2 crystal also comes from compressed CuF64- complexes, although hidden by an additional orthorhombic instability due to a negative force constant of b(2g) and b(3g) local modes. The associated distortion, similar to that involved in K2CuF4 and other layered Cu2+ compounds, is also shown to be developed for ZnF2:Cu2+ upon increasing the copper concentration. The origin of this cooperative effect is discussed together with the differences between non-Jahn-Teller systems like ZnF2:Cu2+ and CuF2 and true Jahn-Teller systems like KZnF3:Cu2+. From present results and those on layered compounds, the usual assumption of a JTE for explaining the properties of d(9) ions in low-symmetry lattices can hardly be right.