The Gemini answer first cites Kaessmann, Wiebe, and Pääbo (1999), which explicitly says it sampled from all 3 at the time recognized major subspecies of chimpanzee (and found it 4x more genetically diverse than humans), not the same patch of forest.
Then it cites Goldberg and Ruvolo (1997), which uses the frankly hilarious "more variation between than within groups" metric. Why hilarious? Because it looks at single genes, while most traits are polygenic. When you look at multiple genes, even with only 2-3 dimensions to display the results (the data has thousands of dimensions), populations can be clearly distinguished [1]. What is the value in such a useless metric? And even then, the paper doesn't state something so extreme - quite the opposite. Direct quote from the paper:
Eastern chimpanzees are not, however, the genetic equivalents of humans. Mean, modal and maximum levels of nucleotide difference are actually slightly lower in eastern chimpanzees than in humans. The last common maternal ancestor of eastern chimpanzees may therefore be even younger than the last common maternal ancestor of all humans.
In fact, even a cursory reading of Gemini's answer shows it to be inconsistent - it states: "In contrast, chimpanzees (Pan troglodytes) exhibit a nucleotide diversity that is often two to four times higher than that of humans, depending on the genomic regions analyzed."
2-4 higher diversity, but there are 4-5 recognized chimpanzee subspecies [2]! Far from "two chimpanzees (implied from the same subspecies) living side-by-side are more different than the two most different humans", it puts humans right on the edge, or slightly past it, of meriting at least one subspecies of our own.
The last study it cites, Fontserè et al. (2022), barely mentions human genetic variation, and doesn't actually provide any quantitative comparisons between it and that of chimpanzees.
Finally, I didn't actually get what I asked for. Nowhere in those articles, or the AI answer, is there anything equivalent to "the genetic distance between Eastern and Western Chimpanzees is X, while the distance between a Norwegian and a Pygmy is Y."
So no, it doesn't actually check out, if you apply minimum scrutiny.
The sibling answer claims the fixation index [F_st, 3] is a measure of genetic distance, but that's not exactly true. E.g. it can't be used to show that dogs are closely related to wolves, less closely to cats, and even less closely to salmon - the F_st for all those comparisons, save perhaps for wolves, would be simply 1. Still, I took your advice, and asked AI (Gemini). I asked:
What is the genetic distance between eastern and western chimpanzees, and how does it compare to the genetic distance between a Spaniard and a Han Chinese?
To summarize its answer (can't share the chat when not logged in, feel free to verify), it claimed the fixation index is used for this purpose, and gave the following numbers:
Western vs. Eastern Chimpanzees F_st = ~0.32
Central vs. Eastern Chimpanzees F_st = ~0.09
Spaniard vs. Han Chinese F_st = ~0.11 – 0.15
The values for the human comparison are more or less in line with [3], but I couldn't find a source for the chimpanzee numbers after a very brief search. I've already spent far too much time debunking a casual AI slop answer.
[1] https://pmc.ncbi.nlm.nih.gov/articles/PMC10113208/
[2] https://en.wikipedia.org/wiki/Chimpanzee#Subspecies_and_popu...
[3] https://en.wikipedia.org/wiki/Fixation_index