Hamilton was dangerous when he had too much to drink. When in his cups, he tended to be loquacious and didn't watch his tongue.
At a dinner party in New York, Hamilton said someting about Burr that was eventually relayed to him, and Burr felt he had no choice but to challenge Hamilton to a duel. The exact content of Hamilton's allegation was a mystery.
In his book Burr, published in 1973, Gore Vidal said that Hamilton had alluded in a stage whisper that Burr was carrying on an incestuous affair with his daughter, which was enough to trigger Burr's fury. Historians of the time charged Vidal with being salacious, but more recent scholarship indicates that Vidal may have gotten it right.
In this case, it was not "In vino, veritas", but "In vino, mortuus."
Sounds like an insult worthy of a knuckledusting but I don’t guess gentlemen did that.