The liver can make some things more water soluble to be excreted via the kidneys, or more fat soluble to be excreted via the gallbladder > stomach > bowel.

I haven’t looked in to it, but I’d hazard a guess that, if this story is true, some of the toxins are excreted via the second route mentioned above, thereby rendering the urine less toxic.

Everyone I’ve known who has consumed amanita muscaria has said something to the effect of “I won’t do that again”. Two mates ended up in hospital for a bit.

Not an extreme sport I’d recommend.