Thick discs are nearly ubiquitous components of the discs of present-day galaxies. It has been proposed that a fraction of their stars have been accreted. Here, we aim to find whether accretion of satellites is the main formation mechanism of thick discs. To do so, we observed a sample of eight nearby edge-on galaxies with the Multi-Unit Spectroscopic Explorer (MUSE) integral field unit at the Very Large Telescope (VLT). Six of the galaxies have a distinct thick disc. We derived thick-disc velocities and velocity dispersions for the galaxies in our sample. We devise a formalism to estimate the fractions of retrograde material in the thick discs by using kinematical maps and thin/thick disc decompositions. None of the galaxies in our sample show strong evidence for retrograde material at large distances from the centre. Including those found in the literature, there are seventeen thick discs with studied kinematics, with only one showing unambiguous signatures of retrograde material. Literature numerical studies of dynamical friction allow us to estimate that at the current cosmic time about one in six mergers for which the stars of the accreted galaxy ended in a thick disc were retrograde. This is in tension with the observed fraction of galaxies with a partly retrograde thick disc (one in seventeen). We conclude that satellite accretion is not favoured by observations to be the main formation mechanism of thick discs.