  The extractions of nuclear charge radii from muonic atom spectroscopy for
$^{40}$Ca and $^{208}$Pb are revisited to analyze the model dependencies
induced by employing a Fermi-type charge distribution. For that, the charge
densities, together with the corresponding muonic transition energies,
calculated by the covariant density functional theory are used as a benchmark.
The root-mean-square deviation of transition energies is calculated to
quantitatively investigate the sensitivities of transition energies to the
details of the two-parameter Fermi distribution. It is found that the second
and fourth moments of the charge distribution can be extracted accurately from
the muonic atom spectroscopy without much model dependencies, whereas the
obtained two-parameter Fermi distributions cannot reproduce the details of the
benchmarking charge densities and, in particular, its surface-diffuseness
parameter cannot be determined accurately with the present experimental
uncertainties on the muonic transition energies.
