Not at all. I've spent plenty of time (sessions exceeding an hour) in saunas that were >105F and >95% humidity (literally so much steam that it was continuously raining from the condensation).

Remember that when you get a fever, your internal body temp can jump to 103+ and stay there for days. Even at a wet bulb temperature above 110, it's going to take time for your internal temperature to heat up to that level. There's nothing "potentially in minutes" about it for humans that are used to the heat.

Sure, you do eventually have to get somewhere cooler. But a wet bulb temperature of 105F is not going to be fatal for a well adapted human even after a few hours.