  Recent studies have made the community aware of scattered light when
examining low-surface-brightness galaxy features such as thick discs. In our
past studies of the thick discs of edge-on galaxies in the Spitzer Survey of
Stellar Structure in Galaxies (S$^4$G) we modelled the point spread function as
a Gaussian. We re-examine our results using a revised point spread function
model that accounts for extended wings out to more than 2.5arcmin. We study the
$3.6\mu{\rm m}$ images of 141 edge-on galaxies from the S$^4$G. We decompose
the surface brightness profiles of the galaxies perpendicular to their
mid-planes assuming that discs are made of two stellar discs in hydrostatic
equilibrium. We decompose the axial surface brightness profiles of galaxies to
model the central mass concentration - described by a S\'ersic function - and
the disc - described by a broken exponential disc. Our improved treatment
confirms the ubiquity of thick discs. The main difference between our current
fits and those presented before is that now the scattered light from the thin
disc dominates the surface brightness at levels below $\mu\sim26\,{\rm
mag\,arcsec^{-2}}$. This does not affect drastically any of our previously
presented results: 1) Thick discs are nearly ubiquitous. They are not an
artefact caused by scattered light as has been suggested elsewhere. 2) Thick
discs have masses comparable to those of thin discs in low-mass galaxies -
circular velocities $v_{\rm c}<120\,{\rm km\,s^{-1}}$ - whereas they are
typically less massive than the thin discs in high-mass galaxies. 3) Thick
discs and central mass concentrations seem to have formed at the same epoch
from a common material reservoir. 4) Roughly 60% of the up-bending breaks in
face-on galaxies are caused by the superposition of a thin and a thick disc
where the scale-length of the latter is the largest. (Abridged)
