You said these sentences are identical in meaning.
- I have a distant relative who was Native American.
- Because I have a distant relative who was Native American I am Native American.
It's clear to me they aren't. I'm saying the first one makes one claim and the second one makes a separate claim. To illustrate, let's take a look at an example.
- I was born in America.
- Because I was born in American I am an American.
Here the second statement claims nothing more than what's claimed in the first. Why? Because it's a fact that being born in America makes you an American. It's also true that if you changed things up it would be false.
- I am an American.
- Because I'm an American I was born in America.
That makes no sense because born in America doesn't necessarily follow from being an American. Immigrants can become Americans. Now let's similarly examine our original statements in a changed up way..
- I am Native American.
- I have a distant relative who was Native American.
If Warren claims she is a Native American then it follows she has NA ancestry (Dances With Wolves notwithstanding). Clearly the second statement offers no more of a claim than the first because it naturally follows. Now back to the beginning.
- I have a distant relative who was Native American.
- Because I have a distant relative who was Native American I am Native American.
It's not a fact that being NA follows from the claim that one has a distant NA relative. As we've seen, it's highly debatable at what point the status of Native American is reached. Tribes don't even do it the same way when making official determinations. So because being NA doesn't necessarily follow from simply claiming to have a distant ancestor, those statements are not claiming the exact same thing. Which means that Warren has in fact claimed more than having a distant ancestor, as evidenced by her minority status claim at UPenn in a link provided by you.