A black hole is expected to end its lifetime in a cataclysmic runaway burst of Hawking radiation, emitting all standard model particles with ultrahigh energies. Thus, the explosion of a nearby primordial black hole (PBH) has been proposed as a possible explanation for the $\sim 220\mathrm{PeV}$ 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 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 h preceding the burst. The absence of any such multimessenger 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.