So how does this work? If I talk to my wife (she is a US citizen, I am European) on the phone about, say for instance, groceries, are the NSA going to listen to it?
Last time I checked, most web services (or even telephone providers) are not keeping track of or verifying nationalities. Thus, any blanket surveillance means they are inadvertently spying on US citizens/persons.
Let's say you have an American, living abroad. He signs up for a Skype account. Skype does not verify nationality or identity. He starts using Skype to call phones in some country the NSA finds suspicious (say, Afghanistan). A dragnet which would intercept these communications automatically would be illegal, as one of the parties was a US Citizen... and they would need a warrant.
The whole thing is ridiculous. The whole question of "do I need a warrant or not" requires you to prove that you do not. But to whom? You are in the pre-warrant phase... Crazy.
But the NSA can certainly listen to his wife's calls... many of which may include him as the other endpoint. This is an obvious edge case even if this legal smoke-screen offered any actual protection, which seems unlikely.
Also, because I don't believe that these policies are worth anything; what really matters are capabilities, and the NSA clearly has whatever access it needs to listen to anyone it wants.