@ Tensor and Lepton
Various papers cite fission being induced by solar energy neutrinos. Nuclei with mass above and below Fe undergo neutrino induced fission according to
http://www.chemistry.bnl.gov/SciandTech/SN/default.htm
Cited are Ytterbium, Gallium, Chlorine and Deuterium. The equation/mechanism for Neutrino capture Yb is given.
Therefore the principle of neutrino-induced fission of a range of nuclei is established.
A recent (2006) summary of Solar Neutrino capture experiments
http://pdg.lbl.gov/2006/reviews/solarnu_s067sol.pdf
Note that the neutrino capture creates unstable nuclei which then decay by fission to lower mass products.
Regarding the new paper on the correlation between decay and Solar flux
While the mechanism is unknown the correlation is real. The writers are being cautious. Neutrino Flux fits with other observations. If not neutrino flux then some other fission-inducing flux is responsible.
In conclusion
It is established that Stellar fusion produces a flux capable of inducing fission. So far it appears there is limited data on the process, and a limited range of nuclei have been observed undergoing neutrino-induced fission. However nuclei with masses ranging from that for Yb to D have been observed interacting.
Quantifying the process over the integrated universe is beyond my scope. I can only suggest that in principle we have a basis for a fission/fusion cycle
For example some capture rates may vanishingly small, but given the scale of the universe, possibly infinite, interactions will eventually occur.