I believe you are right on both counts. And the Declaration of Independence says so, specifically. The founders did believe that all human beings had "inalienable rights" endowed to them by their "Creator". And although we can argue the exact language and meaning, it seems pretty clear to me that they were talking about existential rights: rights that we all have by the fact of our existing. Such as the right to live, the live freely, and to seek our own happiness.
The founders also stated, in that same paragraph, that all human beings have the right to "abolish" their own governments if those governments are not respecting of these unalienable human rights. Again, we can dispute at what point such a thing should occur, and to what degree it becomes warranted, but their position on this was clear enough.
from the Declaration of Independence"
When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.
