Randomness and frustration are believed to be two crucial criteria for the formation of spin glass state. However, the spin freezing occurs in some well-ordered crystals below the related temperature Tf due to the instability of each spin state, which induces the variation of either magnetic moment value or exchange energy. Here we explore the new mechanism of the in-site originated disorder in antiferromagnets Gd0.73La0.27B6 and GdB6, which is caused by the random mutual shifts of Gd3+ spins from the centrally symmetrical positions in the regular cubic lattice. The universal scaling of ESR linewidth temperature dependencies to the power law ΔH(T) ~ ((T - TD)/TD)α with α = - 1.1 ± 0.05 in the paramagnetic phase of both compounds demonstrates the identity of the origin of magnetic randomness. In Gd0.73La0.27B6 the resulting random spin configurations freeze at Tf ≈ 10.5 K where the maximum of magnetization is observed. Below Tf the splitting of ZFC and FC magnetization curves takes place as well as the magnetic state depends on the antecedent sample history. In the case of GdB6 the coherent displacement of Gd ions compete with these random shifts forming an antiferromagnetic (AFM) phase at TN = 15.5 K, which prevails over the spin freezing at Tf ≈ 13 K, expected from the ESR data. The observation of the hysteresis of the ESR spectrum in the AFM phase suggests that its properties may be determined by the competition of two types of AFM orders, which results in formation of stable magnetic domains with nonequivalent positions of AFM Gd pairs at T < 10 K.