  Recent work has confirmed that the masses of supermassive black holes,
estimated from scaling relations with global properties such as the stellar
masses of their host galaxies, may be biased high. Much of this may be caused
by the requirement that the gravitational sphere of influence of the black hole
must be resolved for the black-hole mass to be reliably estimated. We revisit
this issue by using a comprehensive galaxy evolution semi-analytic model, which
self-consistently evolves supermassive black holes from high-redshift seeds via
gas accretion and mergers, and also includes AGN feedback. Once tuned to
reproduce the (mean) correlation of black-hole mass with velocity dispersion,
the model is unable to also account for the correlation with stellar mass. This
behaviour is independent of the model's parameters, thus suggesting an internal
inconsistency in the data. The predicted distributions, especially at the
low-mass end, are also much broader than observed. However, if selection
effects are included, the model's predictions tend to align with the
observations. We also demonstrate that the correlations between the residuals
of the local scaling relations are more effective than the scaling relations
themselves at constraining AGN feedback models. In fact, we find that our
semi-analytic model, while in apparent broad agreement with the scaling
relations when accounting for selection biases, yields very weak correlations
between their residuals at fixed stellar mass, in stark contrast with
observations. This problem persists when changing the AGN feedback strength,
and is also present in the $z\sim 0$ outputs of the hydrodynamic cosmological
simulation Horizon-AGN, which includes state-of-the-art treatments of AGN
feedback. This suggests that current AGN feedback models may be too weak or are
simply not capturing the effect of the black hole on the stellar velocity
dispersion.
