In Oklahoma, apparently, being part Native American is frequently family lore. Whether true or not for Senator Warren has not been confirmed. There is no evidence she claimed being Native American to get better treatment, because, you know, Native Americans are treated so great here, right?
What is the relevance to Navajo heroes in World War II? None. Trump dragged it in because insulting women (and people of color) is how he communicates to his base, like some of the boys on this board. So he disrespects authentic heroes? So what? They are unimportant, to Trump, only he matters.
Suppose Senator Warren did actually lie and receive benefits for being part Native American - I am not conceding this, but suppose for the sake of argument. Remember the white woman, I think name was Rachel Dolean or somesuch, who claimed to be black? Fine to criticize her. Not fine to call her Mammy or Aunt Jemima. Totally not fine to hold a White House meeting to honor, say, the women who wrote computer codes in Hidden Figures, and then drag in "Aunt Jemima out in Seattle would say she was there too, ha ha, isn't that funny".
Normal people understand this. Normal people understand when you are supposed to be honoring someone, you don't drag in an unrelated person, and reference that person with what the group you are supposedly honoring would consider a racial slur against them. Seriously, could you imagine George W Bush, whom I despise and loathe, doing this?
Trump is not normal person.