The word "ought" means a particular thing, refers to a particular function, and once you realize that, ought-statements have truth-values. There's just nothing which says that other minds necessarily care about them. It is also possible that different humans care about different things, but there's enough overlap that it makes sense (I believe, Greene does not) to use words like "ought" in daily communication.

Just a minor thought: there is a great deal of overlap on human "ought"s, but not so much on formal philosphical "ought"s. Dealing with philosophers often, I prefer to see ought as a function, so I can talk of "ought(Kantian)" and "ought(utilitarian)".

Maybe Greene has more encounters with formal philosophers than you, and thus cannot see much overlap?