"On 7 August 2010, Russian finalist and former third-place finisher Vladimir Ladyzhensky and Finnish five-time champion Timo Kaukonen passed out after six minutes in the sauna, both suffering from terrible burns and trauma. According to a spectator who asked not to be identified, Kaukonen was able to leave the sauna with assistance, but Ladyzhensky had to be dragged out, and almost immediately went into cramps and convulsions. Ladyzhensky died despite resuscitation and Kaukonen was rushed to the hospital. He was reported to suffer from extreme burn injuries, and his condition was described as critical, but stable."
When you add water onto dry stones at 110 degrees celsius, the water turns to steam, absorbing some of the heat. This heat abosorbed is known as Latent Heat of Vaporisation / Evaporation. The temperature therefore drops. So temperature drops every thirty seconds by the method described in your link. The steam thus created is not under pressure, thererfore the temperature of the steam will be at 100.
At 1 bar pressure water cannot be heated to over 100 degrees celsius. Steam at 120 will melt your skin and flesh. I did my A level Chemistry project on Latent Heat (there one for the freezing point also)
What you are talking about is the temperature of the rock. Yes the rocks could be far hotter than 120 but that does not mean the steam is. Steam below 100 will condense back into water. So if you are going to split hairs, the temperature in all saunas will be 100 degrees. However when you breathe it in, temperature drops due to the physiological defenses you have.
Problem is your defences can only work for so long as essentially the mechanism for reducing the temperature of steam reaching your lungs is also Latent Heat of water. So once that defence is depleted, then you have a problem. That 30 second limit I mentioned in my last post is most likely wrong -it might be more like a few minutes, reading the articles you have linked.