It is the operating carrier's discretion. When you fly a ticket from, let's say, DEN-ICN with a connection at LAX, you are expected to fly to ICN because that is what the contract is for. You may not legally, although there is little to prevent you physically from using your ticket to simply fly to LAX (this is what hidden city ticketing fraud is all about).

It makes all the sense in the world for the initial carrier to deny boarding for a passenger it determines does not possess the documents for travel.

But, there is certainly nothing wrong with a carrier allowing the passenger to fly the domestic segment, as happened with OP.