Could a Primordial Black Hole Explosion Explain the extremely high-energy KM3NeT neutrino Event?

A black hole is expected to end its lifetime in a cataclysmic runaway burst of Hawking radiation, emitting all Standard Model particles with ultra-high energies. Thus, the explosion of a nearby primordial black hole (PBH) has been proposed as a possible explanation for the $\sim 220$~PeV neutrino-like event recently reported by the KM3NeT collaboration. If the event originated from a PBH, the source would need to lie at $(1-7)\times 10^{-5} \mathrm{pc}$ - depending on the assumed effective area - thus within the Solar System. At such proximity, the resulting flux of gamma rays and cosmic rays would be detectable at Earth. By incorporating the time-dependent field of view of gamma-ray observatories, we show that LHAASO should have recorded $\mathcal{O}(10^8)$ events between fourteen and seven hours prior to the KM3NeT detection. IceCube and KM3NeT \textit{itself} should likewise have detected of order a few hundred events in the range $1~\mathrm{TeV} \lesssim E_\nu \lesssim 1~\mathrm{PeV}$ during the 24 hours preceding the burst. The absence of any such multi-messenger signal, particularly in gamma-ray data, strongly disfavors the interpretation of the KM3-230213A event as arising from evaporation in a minimal four-dimensional Schwarzschild scenario.