Smith and Keynes share a birthday

Or so claims Don Boudreaux over at Cafe Hayek.

In what is surely one of history’s great ironies, today [June 5] is the birthday of both Adam Smith and John Maynard Keynes.

But I don't think there is a great irony here since we don't know Smith's actual date of birth. June 5 is most likely the date of his baptism, not birth. Why that date is on his gravestone as his date of birth no one knows.