Context. X-ray reflection is a very powerful method to assess the spin of supermassive black holes (SMBHs) in active galactic nuclei (AGN), yet this technique is not universally accepted. Indeed, complex reprocessing (absorption, scattering) of the intrinsic spectra along the line of sight can mimic the relativistic effects on which the spin measure is based. Aims. In this work, we test the reliability of SMBH spin measurements that can currently be achieved through the simulations of high-quality XMM-Newton and NuSTAR spectra. Methods. Each member of our group simulated ten spectra with multiple components that are typically seen in AGN, such as warm and (partial-covering) neutral absorbers, relativistic and distant reflection, and thermal emission. The resulting spectra were blindly analysed by the other two members. Results. Out of the 60 fits, 42 turn out to be physically accurate when compared to the input model. The SMBH spin is retrieved with success in 31 cases, some of which (9) are even found among formally inaccurate fits (although with looser constraints). We show that, at the high signal-to-noise ratio assumed in our simulations, neither the complexity of the multi-layer, partial-covering absorber nor the input value of the spin are the major drivers of our results. The height of the X-ray source (in a lamp-post geometry) instead plays a crucial role in recovering the spin. In particular, a success rate of 16 out of 16 is found among the accurate fits for a dimensionless spin parameter larger than 0.8 and a lamp-post height lower than five gravitational radii.