The Monster Manual also establishes this as a default rule, while the PHB couches it as something "most DMs" do.
Basically this. DSTs are a mechanic meant to relay the metagame concept that the PCs are special. This means, among other things, that despite the memes that circulate around, that a DM who has "intelligent monsters double tapping downed PCs" is metagaming.Originally Posted by Monster Manual, page 7