These "Rights" are unalienable. They are not to be given away, they are not to be taken away. Governments exist to secure these rights. To help protect these rights, the government may exist... but only by consent of the people being governed.
It may be true that the Russian government does not give these rights to it's citizens, or that these citizens yield these rights to the Russian government. Nevertheless, according to the morals listed in the DoI, the US government is founded on the belief that Russians have these rights, because they are human beings.
Therefore, the US government, when dealing with 'men' of any nationally, needs to respect the unalienable Rights which all men have been granted by their Creator. Anything else is hypocritical.
Edit: after thinking about it, it gets even better. Because foreigners have not consented to being governed by the US, the rights of foreigners not to be spied on by the US government would go even further than the rights of Americans. And yes, I know the DoI is not law. But if we Americans cannot simultaneously claim to believe in it's principles and make laws that contradict it without being hypocritical.