The coupling between accretion processes and ejection mechanisms in accreting black holes in binary systems can be investigated by empirical relations between the X-ray/radio and X-ray/optical-infrared luminosities. These correlations are valid over several orders of magnitude and were initially thought to be universal. However, recently, many black hole binaries have been found to produce jets that, given certain accretion-powered luminosities, are fainter than expected from the earlier correlations. This shows that black holes with similar accretion flows can produce a broad range of outflows in power, suggesting that some other parameters or factors might be tuning the accretion–ejection coupling. Recent work has already shown that this jet power does not correlate with the reported black hole spin measurements. Here we discuss whether fixed parameters of the binary system (orbital period, disc size, inclination), as well as the properties of the outburst, produce any effect on the energy output in the jet. No obvious dependence is found. We also show that there is no systematic variation in the slope of the radio–X-ray correlation with normalization. We define a jet-toy model in which the bulk Lorentz factor becomes larger than ˜1 above ˜0.1 per cent of the Eddington luminosity. With this model, if we assume random inclination angles which result in highly variable boosting at large Eddington ratios, we are able to reproduce qualitatively the scatter of the X-ray–radio correlation and the ‘radio-quiet’ population. However, the model seems to be at odds with some other observed properties of the systems. We also compare the ‘radio-quiet’ black holes with the neutron stars. We show that if a mass correction from the Fundamental Plane is applied, the possibility that they are statistically indistinguishable in the X-ray–radio plane cannot be completely ruled out. This result suggests that some of the outliers could actually be neutron stars or that the disc–jet coupling in the ‘radio-quiet’ black holes is more similar to the one in neutron stars.