Because the two derivations provided at your reference work!
"...most systems at high temperatures obey the classical (Maxwell–Boltzmann) limit unless they have a very high density, as for a white dwarf. Both Fermi–Dirac and Bose–Einstein become Maxwell–Boltzmann statistics at high temperature or at low concentration..."
It also depends on what your mean by "correct"...."approximately correct" would perhaps be a better description.... did you see the "limits of applicability"...??
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