As I recall from my one relatively brief trip to Greece, the Arenaria-like plants were identified by our tour leader (John Richards, former Pres. AGS) as
Minutaria species. They're very close after all and I suspect in some cases could be synonymous. We were in the general areas of Mt Parnassus, Mavrolithari and Karpenessi.
If you were in NZ I'd say for sure, that the Arenaria plant was
Scleranthus uniflorus