I spent much of my life living in that temperature range without A/C, working outside during the day in the sun.
It's hot but not going to kill you. In fact, there are massive homeless encampments outside my window right now in extremely humid, hot, Texas weather (it is 95-97 all week and very human). The homeless have endured many summers like this.
It is a massive stretch to say these temperatures are not survivable. They are not healthy in the long run - but neither is sun exposure.
It's an incredible exaggeration to say Chicago (where 600 people died in the heat wave) is not survivable at all when millions actually did survive the heat wave without AC.
If a major city has such a heatwave, it will almost certainly be a mass casualty event, mitigated only by the duration of the wave and how many people have A/C (or how long the blackouts last).
A fan won't work because your sweat will not evaporate: in fact it just heats you up faster (like breathing on your skin in a sauna).
Such temperatures have only been measured a few times on earth, so no, you have not experienced them.
At quick check, humidity in Houston is like 55%, so the wet-bulb temperature is only ~80f. Uncomfortably hot, but not close to the threshold discussed in TFA.