POEMMA-Balloon with Radio (PBR) is a scaled-down version of the Probe
Of Extreme Multi-Messenger Astrophysics (POEMMA) design, optimized to
be flown as a payload on one of NASA's sub-orbital super pressure
balloons circling the Earth above the southern oceans for a mission duration of
more than 20 days. One of the main science objectives of PBR is to
follow up astrophysical event alerts in search of neutrinos with very
high energy ($10^8 \lesssim E_\nu /{\rm GeV} \lesssim 10^{10}$). Of particular
interest for anticipated PBR observations, the KM3NeT Collaboration has recently reported the detection of the neutrino KM3-230213A with $10^{7.8} \lesssim E_\nu/{\rm GeV} \lesssim 10^{9.0}$. Such an unprecedented event is in tension with upper limits on the cosmic neutrino flux from IceCube and the Pierre
Auger Observatory: for a diffuse isotropic neutrino flux there is a
$3.5\sigma$ tension between KM3NeT and IceCube measurements, and about $2.6\sigma$ if the neutrino flux originates
in transient sources. Therefore, if
KM3-230213A was not beginner's
luck, it becomes compelling to consider beyond Standard Model (BSM)
possibilities which could lead to a signal at KM3NeT-ARCA but not at
IceCube/Auger. We calculate the PBR horizon-range sensitivity to probe
BSM physics compatible with observation at KM3NeT-ARCA and
non-observation at
IceCube/Auger. As an illustration, we consider a particular class of BSM physics models which
has been described in the literature as a possible explanation of KM3-230213A.