When it comes to fungi then I think care is needed in interpreting the evidence. Current phylogenetic data indicate at least 3 distinct taxa under the name Galerina marginata. One appears to be distributed across Europe and the (eastern?) USA, another across Asia and (western?) USA and a third in Australasia. This is the usual picture for fungi, where traditional morphological specie concepts often don’t uniquely match phylogenetic concepts. So the potential global distribution of a ‘species’ depends highly on what you define as a species.