That might be true, but that wasn't really their point.

Being accurate is less important than trying to get the lie out in front of as many eyeballs as possible, so the lie can be repeated in front of people who might not realize this sort of information offhand.

I spent a good minute thinking of the best reply. You're right, the truth was immaterial to them and they were posting in bad faith. Proving that this is the result of cooperation, to me, was the quickest way to unravel the rest of their post.