Very late response but wanted to clarify, I'm not saying it's the duty of the US government to actively protect the rights of the entire population of the world. That's actually quite a radical perspective (I always found the 'bring them freedom' argument for invading Iraq quite an interesting position for conservatives to take).

But what I instead mean is that if the US government interacts with non-citizens outside of its own borders (as it often does), shouldn't it respect the the 'inalienable' rights 'all men' have? That would preclude them from engaging in torture, detention of non-combatants without trial, mass surveillance of foreigners, etc.

What I mean is that it shouldn't matter if a person is a US citizen or not; if the US government is interacting with people, it should respect the rights it believes all people to intrinsically have. Again, that is different than proactively 'bringing' people those freedoms.