  In this letter, the Grey-Disk and the Core-Corona models are combined in a
scenario that aims to explain different unexpected features observed in the
interactions of the highest energy particles in the Earth's atmosphere. In
particular, the observed distributions of $X_{\rm max}$ and $N_\mu$ are
explained, assuming that the ultra-high-energy cosmic ray spectrum is dominated
by protons produced by a few extra-galactic sources with different injection
spectra and maximum energy cutoffs. The compliance of this heterodox scenario
with other relevant observations as the instep region in the energy spectrum,
the event-by-event correlations between $X_{\rm max}$ and the detected signal
at the ground and the absence of detection, so far, of UHE neutrinos or
photons, are also briefly discussed. If confirmed, such a scenario would
dramatically change the present understanding of the UHECR primary composition
and, thus, the characteristics of their sources.
