That's not entirely correct. During meiosis ( the cell division process that reduces chromosomes in sperm and egg cells to half the number in somatic cells), somatic chromosomes (and X chromosomes, IIRC) undergo "crossover" in which bits of the corresponding chromosomes are exchanged, so individual chromosomes in sperm and egg cells are not entirely from one parent, but are a mixture of those from both parents. So, while it is possible that no DNA would remain from a distant ancestor, the probability of that is considerably lower than it would be if only whole chromosomes went into sperm and egg cells.
I agree with Random's main point, though: there's only so many traceable units, and over time, genuine ancestry may vanish. Also, we're assuming nuclear autosomal DNA. If the candidate allele is in mtDNA, then any male in the lineage would break the chain of transmission. If it's nuclear but not autosomal, there's very little crossover between X and Y (it's restricted to the very trace pseudoautosomal regions), so sex selection has a statistically strong impact on allele eliminations.
Assume for the moment that there is such a thing as an Amerind allele (there isn't) on an autosomal nuclear chromosome - there's a 50% chance of passing that onto offspring. So, if her 'mixed' grandparent was metis (50% chance) then it may have passed to a parent (25% chance) and herself (1/8th chance) means there's an 88% chance that she could have no genetic trace of that allele AND be descended from an amerind. What information would a DNA test provide for supporting this type of claim? Confirmatory maybe, but disconfirmatory, no.
(The math gets more complex if there's more candidate alleles.)
More on the alleles and how retail/consumer DNA testing kits use them. They do not publish their proprietary formulations, and we know that the results from identical samples give different results in different services, and even different results over consecutive years from any single service. This strongly implies they're using statistical modelling, and trying to adapt based on the published literature.
For myself when I submitted tests for my local skeptical group (as a healthfraud investigation), I focused on a specific allele to try to reverse engineer their algorithms. There's no gene that is 100% a marker of an ethnic group. There are some that are mostly in one, and scarce in others, which is close but not conclusive. In my case, it was an allele that I used to investigate if I might have Ashkenazi ancestry. Typically, it's dominant in Ashkenazi, but exists in smaller incidence everywhere. Africans have it. Amerinds have it. Asians have it. It's just that if a person has it, the results are 99% confidence the person is Ashkenazi, knowing nothing else.
But it's the 'knowing nothing else' that is the trick. If I'm an australian aborigine with that gene, and no family history, then probably it's not Ashkenazi ancestry, looks like an independent de novo.
So, in Warren's case, she has a verbal family history that could overrule a negative finding for one candidate Amerind allele, since there's almost a 90% chance that a genuine Amerind descendant would not have that allele anymore after so many generations.