  We investigate the possibility that blazars in the Roma-BZCAT Multifrequency
Catalogue of Blazars (5BZCAT) are sources of the high-energy astrophysical
neutrinos detected by the IceCube Neutrino Observatory, as recently suggested
by Buson et al. (2022a,b). Although we can reproduce their $\sim 4.6\, \sigma$
result, which applies to 7 years of neutrino data in the Southern sky, we find
no significant correlation with 5BZCAT sources when extending the search to the
Northern sky, where IceCube is most sensitive to astrophysical signals. To
further test this scenario, we use a larger sample consisting of 10 years of
neutrino data recently released by the IceCube collaboration, this time finding
no significant correlation in either the Southern or the Northern sky. These
results suggest that the strong correlation reported by Buson et al. (2022a,b)
using 5BZCAT could be due to a statistical fluctuation and possibly the spatial
and flux non-uniformities in the blazar sample. We perform some additional
correlation tests using the more uniform, flux-limited, and blazar-dominated
Radio Fundamental Catalogue (RFC) and find a $\sim 3.2\sigma$ equivalent
p-value when correlating it with the 7-year Southern neutrino sky. However,
this correlation disappears completely when extending the analysis to the
Northern sky and when analyzing 10 years of all-sky neutrino data. Our findings
support a scenario where the contribution of the whole blazar class to the
IceCube signal is relevant but not dominant, in agreement with most previous
studies.
