If two people are lynched on the same day, fake weakness selects one of them at random to be the fake leech target. Internet Flea's deception wouldn't have been revealed if the double lynch had happened, but it would have seemed a bit odd for him to leech a player and then lead a lynch on that player.

Generally, it's probably a bad idea for people who use fake weakness to lead lynches, but a double lynch led by anybody else would have been perfectly fine.