From exploratory studies and theoretical expectations it is known that simplifying approximations in spectroscopic analysis (local thermodynamic equilibrium (LTE), 1D) lead to systematic biases of stellar parameters and abundances. These biases depend strongly on surface gravity, temperature and, in particular, for LTE versus non-LTE (NLTE), on metallicity of the stars. Here we analyze the [Mg/Fe] and [Fe/H] plane of a sample of 326 stars, comparing LTE and NLTE results obtained using 1D hydrostatic models and averaged <3D> models. We show that compared to the <3D> NLTE benchmark, the other three methods display increasing biases toward lower metallicities, resulting in false trends of [Mg/Fe] against [Fe/H], which have profound implications for interpretations by chemical evolution models. In our best <3D> NLTE model, the halo and disk stars show a clearer behavior in the [Mg/Fe]-[Fe/H] plane, from the knee in abundance space down to the lowest metallicities. Our sample has a large fraction of thick disk stars and this population extends down to at least [Fe/H]~-1.6dex, further than previously proven. The thick disk stars display a constant [Mg/Fe]~0.3dex, with a small intrinsic dispersion in [Mg/Fe] that suggests that a fast SN Ia channel is not relevant for the disk formation. The halo stars reach higher [Mg/Fe] ratios and display a net trend of [Mg/Fe] at low metallicities, paired with a large dispersion in [Mg/Fe]. These indicate the diverse origin of halo stars from accreted low-mass systems to stochastic/inhomogeneous chemical evolution in the Galactic halo.