We compute the spectra of cosmic-ray (CR) nuclei and anti-nuclei 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 60-450GeV 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 $\sim$\,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 over the standard astrophysical background. Furthermore, the total antinuclei flux from interstellar 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.