From what I've seen most of what we have today of the Greek classics (the Iliad, Elements, etc.) are based off translations into Latin or Arabic of the original Greek papyrus scrolls.

What you've seen is either grossly incorrect or you're misunderstanding what it says. Western scholars in the Middle Ages knew a not-insignificant number of Greek texts through Latin or Arabic translations, but we do not. We know them through Greek copies of the Greek texts, the same way we know Latin texts through Latin copies of the Latin texts. Only a couple texts of our very many surviving copies--not even including papyri--are only known from translation. Papyri simply do not survive very long, they are quite fragile. Manuscripts had constantly to be copied in antiquity. Once Greek manuscripts from the Byzantine east became available to western medieval scholars they had access to the Greek