It is shown that the picture of a quasi-2D electron liquid (interacting electron gas) for the quantum oscillations in high magnetic fields is not in agreement with the transverse magneto-conductivity theory (based on the Kubo formalism deduced for an electron gas) including the influence of the many-body self-energy. The enhancement of all energy splittings above their bare value from the difference of the self-energy is automatically zero for the level coincidences in the intra-Landau level cases and, to a high degree, vanishes for the 'spin level coincidences' where levels of different Landau quantum numbers are involved. In contrast, the model of an electron crystallisation in quantising magnetic fields, including lossless edge currents, allows a comprehensive explanation of all current experimental data, where for two occupied lattices near the Fermi energy with 2/3 and 1/3 filling, respectively, effectively an enhancement of the valley splitting results from the diamagnetic energy of both opposite magnetic moments, due to the lossless edge currents (orbit-orbit interaction), and from the Zeeman energy of each spin interacting with the magnetic moment of the orbital edge current of the other lattice (spin-orbit interaction). The many-body self-energy, in the crystalline state corresponding to the binding energy, loses significance compared to that of an interacting electron gas owing to the lossless edge currents which actually enhance the valley splitting and adjust the energies for a 2/3/1/3 filling (or 1/0 occupation for complete separation) of both quantum levels neighbouring the Fermi energy.