I do not understand why someone should think that the QFLs will be always above and below the band edges; indeed, it must be always the other way round since the position is dictated (for example, for QFL for electrons) by the logarithm of the ratio of electron concentration and the effective density of states in CB, whereby the concentration of electrons can never be higher than the effective density of states in CB, therefore the QFL for electrons must be always below the CB edge. Similarly, the QFL for holes will be always above the VB edge.
This is of course fully in agrement with what we expect, since the splitting of QFLs gives you the maximum free energy per electron-hole pair, in other words the maximum useful work that can be extracted from the system, which will be definitely lower than the overall internal energy of electron hole pairs (bandgap energy + 3kT) due to the Second Law of Thermodynamics.