Yes, as a legal matter that is true.
Suppose a person has a green card. When he goes back to his home country, let's say he's arrested, killed and his body cut into pieces with a bone saw. The home country says, "we were just applying our law to our citizen." According to your logic/Trump logic, that's the end of the story -- the US has no interest here, because he's a citizen in the country where his citizenship lies.
Is that how you think the legal system works here?
And think about extradition: when a non-citizen commits a crime on our soil, and then flees back home, can the US extradite him, to try him for his crimes here? The answer is yes. And while the US cannot *compel* that return, the US has every expectation that he will be extradited (per extradition treaties).