I suspect that the saying came long before the sixteenth century.
It is used in the Benjamin Jowett translation of Plato's 'Symposium'.
Plato wrote 'Symposium' about 350 years before the birth of Christ - but, not speaking ancient Greek myself, I am not sure if it is a literal translation of one of Plato's phrases or just or interpretive.
However, as Jowett was a Greek specialist and Master of Balliol College Oxford in the latter part of the 19th century, you can assume he knew his stuff.
Significantly, though - even the translation describes the phrase as a proverb - so it may have been around in common use even before Plato's time.
The translated line in question goes:
"But what follows I could hardly tell you if I were sober. Yet as the proverb says, 'In vino veritas'..."