It matters because your assertion above that 'There might not have been a Greek nation at the time but there were Greeks!' is not accurate in any emotional sense relevant to this thread. To take an instance of what I mean: suppose that in 2½k years a similar question should arise about some present European artefact held in an Oceania museum was requested back by the then pan-European government which represented a population largely consisting of interbreeders with various immigrant incomers from all over in the interim - you would have an analogous situation.

At the time of Pericles & Phidias & the building of the Parthenon; it was done, not by the Greeks as any sort of entity, but by the State of Athens, who were distinct culturally and politically from all the other City States - Corinth, Sparta, Mycenae, &c. It is unconvincing for the present Greek government to put in this claim solely on the grounds that they are directly descended purely from that Athenian entity.

~M~