DNA analysis providing evidence of Native American heritage?

https://www.theguardian.com/us-news/2018/oct/16/donald-trump-elizabeth-warren-dna-test

Genealogical DNA testing is in the news lately. The test results from a DNA test made public by Senator Elizabeth Warren resulted in the following statements from the President of the United States as quoted in the above article from The Guardian.

Referring to her by the racist moniker Pocahontas, Trump said: “She took a bogus DNA test and it showed that she may be 1/1024 [Native American,] far less than the average American …

"Now that her claims of being of Indian heritage have turned out to be a scam and a lie, Elizabeth Warren should apologize for perpetrating this fraud against the American Public,”

Hmm.  These comments and the rest of the controversy have elicited the following response from my expert genealogist daughter, Amy Tanner Thiriot posted on Facebook:

I've talked about the fight over Senator Elizabeth Warren's genealogy from time to time, and the woefully offensive campaign to mock her family stories and heritage. Yes, she has indigenous ancestry, and no, there never has been and never will be any excuse for anyone calling her "Pocahontas" or — more importantly — for using Native American identity as an insult or political weapon. And just in case you've heard otherwise, her political enemies are wrong about her ever being a "diversity hire." If your news outlet is telling you otherwise, you may want to find a new source for news.

Here are a few of the issues raised by the statements made by the President:

• Were the results of a genealogical DNA test "bogus?"
• Does the "average American" have Native American DNA?
• What is the percentage necessary to establish Native American ancestry or any other ancestry?
• What source did the President use to conclude the percentage of Native American ancestry in Elizabeth Warren's test?
• Are claims of Native American ancestry (or any other ancestry for that matter) based on a genealogical DNA test a "lie and scam?"
• Are the genealogical DNA testing companies perpetuating a fraud on the "American Public?"
• Is calling someone a "Pocahontas" now another racist moniker? What about those people who claim descendency from Pocahontas or Rebecca Rolfe?
• Is there something wrong with acknowledging Native American ancestry?

There are probably a lot of other questions that could be raised by these irresponsible statements. The real question from a genealogical standpoint is why is this an issue at all?