We present a comprehensive study addressing pile-up effects in single photoelectron counting with R-11265 Hamamatsu multi-anode photomultiplier tubes (MAPMTs) equipped with the SPACIROC-3 ASIC. Extended dead time in the electronics causes saturation and quenching of the counting rate, an effect we counter by inverting the pile-up plot once the double pulse resolution is determined. Our work combines extensive numerical simulations with experimental validations to quantify the statistical uncertainties associated with the corrected event rates. We apply this methodology to the Mini-EUSO experiment onboard the International Space Station where machine learning techniques are employed to extract pixel-by-pixel double pulse resolutions from long-term photon count histograms. This integrated approach enables the accurate recovery of true photon fluxes essential for studying ELVES, meteors and other transient phenomena detected by Mini-EUSO.