The Peter passage is to remind us that christians are always strangers and pilgrims. Our true home is in heaven not the USA. Christians are in every country not just the USA, so this passage appeals to them as well
If you are suggesting that our government is based on the Declaration of Independence, then you are mistaken. The United States government was first based on the Articles of Confederation (written in 1777 and ratified in 1781) and then upon the Constitution (1789).
Moreover, public sentiment toward established religion changed dramatically after the Revolutionary War was completed. It's easy to assume that no one learned anything and that no opinions changed, but that's far from the truth.
I also prefer the "First Nation" nomenclature, but I am primarily addressing a U.S. audience with my words, not our Canadian friends, so I try to stick with terms that won't make people think I'm not a native-born Texan and U.S. citizen. :)