From what I understand, the reindeer do not receive the same toxic effects that people do with raw Amanitas. The reason it was good to drink their urine is because there are two main psychoactive compounds in the Amanitas: muscimol and ibotenic acid. Muscimol is the hallucinogen, and ibotenic acid is a prodrug that converts to more muscimol after it is ingested. However, ibotenic acid is also a neurotoxin and is likely the reason for what people call the "deliriant" effects. It agonizes NMDA receptors which causes overstimulation and excitotoxicity (killing nerve cells), and that likely adds a very heavy and unpleasant mindfuck. Muscimol, however, is not metabolized at all - it is excreted in urine as muscimol. So if the mushrooms were to pass through the reindeers' bodies first, I imagine what would remain would be nothing but muscimol. The Amanitas can also be cooked properly to turn all of the ibotenic acid to muscimol anyway, so no reindeer are required for a good trip from it. It's possible to get pleasant effects from just eating them raw too, but less likely. The ratios of muscimol to ibotenic acid will vary a lot depending on the mushroom.