Ah, that quote helps me see one of the issues causing confusion! That talks about the lethal dose of phalloidin, which is not the main toxin we usually worry about (it’s not as toxic and it’s deactivated by cooking). The amanitins, mainly alpha-amanitin, are the main ones that cause problems in the dangerous Amanitas, because they’re active even after cooking and take less of a dose. 0.1 mg/kg is probably a good estimate of the LD50 for alpha-amanitin.
That said, estimating a lethal dose of fresh mushroom flesh is far from an exact number. It can depend on the person eating (how large their body is, how healthy their liver is), the mushroom (taxon, age, and ecogeographic factors all cause variation, while different individuals from the same population can have variable amounts of toxin, and different parts of the same mushroom even vary in their toxin amounts), and the speed / kind of medical interventions eventually taken. The amount of water in mushrooms is also hugely variable and complicates any numbers using fresh weight instead of dried weight. My first published paper was actually studying the amount of toxins in the spores vs stalk vs cap of destroying angels (A. virosa).
From the literature I’ve read, the “less than a single cap can kill” advice is undoubtedly wise but perhaps a better-safe-than-sorry extreme. For kids, sure. But adults may need more tissue to kill their liver. Yilmaz et al. 2015 documented a case where a 67 kg man needed hospitalization to save his life after eating two whole caps, ~45 g of fresh tissue, which they considered a rather low dosage.