  We compute the spectra of cosmic-ray (CR) nuclei and antinuclei under a
scenario where hadronic interaction processes inside supernova remnants (SNRs)
can produce a diffusively-shock-accelerated "source component" of secondary
particles. This scenario is able to explain the recent measurements reported by
AMS on the antiproton/proton ratio, that is found to be remarkably constant at
~60-450 GeV of kinetic energy. However, as we will show, this explanation is
ruled out by the new AMS data on the B/C ratio, which is found to decrease
steadily up to TeV/n energies. With the constraints provided by the two ratios,
we calculate conservative (B/C driven) and speculative (pbar/p driven)
SNR-induced flux contribution for the spectra of antideuteron and antihelium in
CRs, along with their standard secondary component expected from CR collisions
in the interstellar gas. We found that the SNR component of anti-nuclei can be
significantly large at high-energy, above a few ~10 GeV/n, but it is always
sub-dominant at sub-GeV/n energies, that is, the energy region where
dark-matter induced signals may exceed the standard astrophysical background.
Furthermore, the total antinuclei flux from insterstellar spallation plus
SNR-component is tightly bounded by the data, so that hadronic production in
SNRs has a minor impact on the astrophysical background for dark matter
searches.
