The local vs remote worker argument works when there's something inherently preferable about the local worker, like you and him are cousins or form the same tribe, or something like that. But nationalism aside, isn't everybody entitled to the same opportunities?
Free trade agreements are negotiated painstakingly to make the treatment of investments uniform across countries. In the process, they usually accord some special treatment to professional classes. I myself am a beneficiary of such rules -- as a Canadian professional, I can skip across the border to the USA with just a little bit of documentation.
We don't have anything equivalent for labor. This seems to me to be a great omission, if not an outright scam. Even after free trade between the US and Canada and Mexico, we don't allow workers to cross borders. Nor do we have uniform standards for the treatment of labor like we do for capital, either.
It seems to me to be deliberate -- they want the workers to be stuck with the local situation, and they want local governments to compete on lowering benefits and labor standards.
I live in San Francisco. When the big earthquake hits and someone has to pull me out of the rubble, they won't be outsourcing that job to the Philippines. It'll be some guy who lives near me, probably the kind of guy with a broad back and an unironic mustache, who has to make do with underemployment since all the local jobs seem to be for douchebags with iPhones.
Do I owe the local worker a living? Of course not. But we both pay taxes to the same government, and he is getting shafted due to China's MFN status, and I as a professional who can afford iPhones am getting an awesome deal.