  The IceCube Collaboration has recently reported compelling evidence of
high-energy neutrino emission from NGC~1068, and also mild excesses for NGC
4151 and CGCG420-015, local Seyfert galaxies. This has increased the interest
along neutrino emission from hot-corona surrounding the super massive black
holes of Seyfert Galaxies. In this paper, we revisit phenomenological
constraints on the neutrino emission from hot-coronae of seyfert galaxies,
using an assumption of equi-ripartition between cosmic-rays and magnetic energy
densities. We show that not only these sources are consistent with such an
assumption but also that the data point towards low beta plasma parameters
inside Seyfert Galaxies. We exploit this finding to constrain the Seyfert
diffuse neutrino flux and we obtain that, in order not to overproduce
neutrinos, not all the sources can be in an equi-ripartition state. We conclude
(along with previous findings) that seyfert galaxies cannot explain the diffuse
neutrino spectrum above $\sim 100\, \rm TeV$, allowing space for other
astrophysical sources.
