They possibly undergo some reaction in the reindeer's liver to break them down, before excreting them in urine.
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.
https://en.wikipedia.org/wiki/Ibotenic_acid
Amanita Muscaria contains muscimol and ibotenic acid. Ibotenic acid is neurotoxic and a prodrug to muscimol, which has the desired psychoactive effect.
There's a theory out there that 'bitter tasters' are an evolutionary adaptation by our Eastern European forebears who lived in an area where alkaloid levels were high in soils. If you avoided alkaloid-embittered foods your liver lasted longer, and so your genes were better represented.