The first results from the STARDUST mission revealed that refractory phases formed at a close distance from the nascent Sun have been transported to the comet forming region. Such refractory phases from meteorites (that originate from the asteroid belt), hold the ashes of Short-Lived Radionuclei (SLR) that were alive in the early solar system (ESS). We show that global energetic constraints obtained from X-ray observations of young stellar objects strongly limit the amount of SLR that can be produced by nonthermal nucleosynthesis (irradiation) in the ESS. We show that 10Be and 41Ca can indeed be produced at levels compatible with a homogeneous distribution over the entire protoplanetary disk up to the comet forming region, but not 7Be, 26Al, 36Cl, and 53Mn. The maximum amount of irradiation-induced 26Al can barely account for a homogeneous rocky reservoir of 2 3 Earth mass. We show here that, even considering a heterogeneous distribution of 26Al in the ESS, an irradiation origin of this preeminent isotopic chronometer is unlikely.