Many relevant properties (including superconductivity and colossal magnetoresistance) of layered materials containing Cu2+, Ag2+, or Mn3+ ions are commonly related to the Jahn-Teller instability. Along this line, the properties of the CuF64- complex in the K2ZnF4 layered perovskite have recently been analyzed using a parametrized Jahn-Teller model with an imposed strain [Reinen, D. Inorg. Chem. 2012, 51, 4458]. Here, we present results of ab initio periodic supercell and cluster calculations on K2ZnF4:Cu2+, showing unequivocally that the actual origin of the unusual compressed geometry of the CuF64- complex along the crystal c axis in that tetragonal lattice is due to the presence of an electric field due to the crystal surrounding the impurity. Our calculations closely reproduce the experimental optical spectrum. The calculated values of the equilibrium equatorial and axial Cu2+-F- distances are, respectively, R-ax = 193 pm and R-eq = 204 pm, and so the calculated distortion R-ax - R-eq = 11 pm is three times smaller than the estimated through the parametrized Jahn-Teller model. As a salient feature, we find that if the CuF64- complex would assume a perfect octahedral geometry (R-ax - R-eq = 203 pm) the antibonding a(1g)*(similar to 3z(2) - r(2)) orbital is placed above b(1g)*(similar to x(2) - y(2)) with a transition energy E((2)A(1g) --> B-2(1g)) = 0.34 eV. This surprising fact stresses that about half the experimental value E((2)A(1g) --> B-2(1g)) = 0.70 eV is not due to the small shortening of the axial Cu2+ - F- distance, but it comes from the electric field, E-R(r), created by the rest of the lattice ions on the CuF64- complex. This internal field, displaying tetragonal symmetry, is thus responsible for the compressed geometry in K2ZnF4:Cu2+ and the lack of symmetry breaking behind the ligand relaxation. Moreover, we show that the electronic energy gain in this process comes from bonding orbitals and not from antibonding ones. The present results underline the key role played by ab initio calculations for unveiling all the complexity behind the properties of the model system K2ZnF4:Cu2+, opening at the same time a window for improving our knowledge on d(9), d(7), or d(4) ions in other layered compounds.