Is "You wouldn't distill..." the hot new Twitter meme or something?

It's a riff on the classic MPAA slogan during the Napster / BitTorrent era, "You wouldn't download a car."

... Yes I would.

It's free real estate.

That was not actually the ad, that was "You wouldn't steal a car. [...] Downloading Pirated Movies is stealing. [...] Piracy it's a crime."

Easily misremembered and meme-able.

The “misrememberance” is describing what the words actually communicated. It’s not incorrect, it’s pointing out the logical flaw in the claim.