False on at least Fedora Atomic^[1]^, NixOS^[2]^ and openSUSE Aeon^[3]^…
Which ‘immutable’ distros are you referring to?
On Fedora Atomic, changing /etc is literally identical to how it goes any other distro; or at least 1-to-1 as on traditional Fedora. The bonus is that a pristine copy of the original /etc is kept inside a sub-directory of /usr. Furthermore, all changes compared to the pristine copy are kept track of.
On NixOS, changes have to be applied through configuration.nix. Though, regardless, it’s effectively possible to edit and populate /etc like it is on other distros.
It’s explicitly mentioned that /etc does not belong to the immutable base.