Recent studies have made the community aware of the importance of accounting for 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 - the S4G - we modelled the point spread function as a Gaussian. In this paper we re-examine our results using a revised point spread function model that accounts for extended wings out to more than 2\farcm5. We study the 3.6 μm images of 141 edge-on galaxies from the S4G and its early-type galaxy extension. Thus, we more than double the samples examined in our past studies. 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 Sérsic function - and the disc - described by a broken exponential disc seen edge-on. Our improved treatment fully confirms the ubiquitous occurrence of thick discs. The main difference between our current fits and those presented in our previous papers is that now the scattered light from the thin disc dominates the surface brightness at levels below μ 26 mag arcsec-2. We stress that those extended thin disc tails are not physical, but pure scattered light. This change, however, does not drastically affect 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 - with circular velocities vc< 120 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) Approximately 50% 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. Data of Figs. B.1 and C.1 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/610/A5