I'm both surprised and skeptical. It makes me wonder whether there's a larger story, now lost... Perhaps the archetypal occurrence was someone famously humorless, and their outburst was forever burned into the minds of those present. Or perhaps the first instance was on the estate of a noble who thought it funny and insisted everyone else find it funny, too...

You might know this already given your username, but for the sake of the thread I feel I should mention "Ha ha" is a common expression in french when discovering something, and not exclusive to this feature (which I felt wasn't made clear in the article). It has a specific intonation pattern and doesn't sound much like laughing, so to me the etymology isn't all that surprising.