Reindeer are a crucial resource in many parts of northern Siberia where the mushrooms are used, so the indigenous people are familiar with reindeer's habits and behaviors. It is well-known that reindeer love fly agarics, and become inebriated after eating them, just as humans do. It might well be that humans in the region thousands of years ago first learned of the mushroom's psychoactive effects effects by watching the reindeer.
But reindeer also have a great thirst for human urine, especially in the wintertime, presumably because it contains essential minerals lacking from their meager diet. This is well-known by the locals, who will urinate as a means of rounding up reindeer that have strayed from the herd, and the reindeer apparently even fight over which gets to lap up the yellow snow. It is not so far-fetched to imagine that the connection between the reindeer, the mushrooms, and human urine somehow led to the discovery that the urine of one who has eaten the fly agaric is nearly as potent as the fly agaric itself. (Letcher 2007) Perhaps some reindeer were observed to be intoxicated after drinking urine from a celebration where the guests were drinking mushroom liquor. Or perhaps some shaman, inebriated by the mushrooms and channeling the spirit of the reindeer, decided to consume his own urine in immitation, and found the property that way. This is all simply speculation, but the pieces seem to fit. Nowhere else in the world does the practice of drinking urine seem to be catching on, although contemporary reports indicate that the occasional intrepid psychonaut isn't averse to trying it.