About biblical authenticity- Greek & Latin?

[Cassius Tullius]

In the past and over the Easter Holiday I've encountered people who claim that their particular interpretation of Holy Writ was derived from the Greek. This is stated to give more authority to their position on whatever religious point they are trying to get across. I understand that the New Testament was put into Greek before being disseminated in Latin.
Is there a specific text or is there a specific collection of texts, in Greek, that give special authenticity to latter translations?