The fact that there was an original version of a quote doesn't make the original version any more "true," so I've never quite understood the instinct of people to use it as some kind of gotcha.

Indeed, if anything it seems like in general the opposite would be true, if common culture adapts a quote to more accurately fit their reality (irrespective of whether this particular quote is "true" or not).

(Also, I can't find any source for your claim, despite plenty of articles on the source of the phrase, such as https://quotes.yourdictionary.com/articles/who-said-absence-..., so I'm guessing that's a myth.)