This is India. A lot of people just don't live close to a body of water. Getting any water is a huge issue.

Can you imagine millions of people running to cool in the river? What with elderly and children?

It depends because wet bulb temperature is normally significantly below ambient temperature. If ambient temperature was 45C a large body of water might be at 38C while wet bulb was 36C. At which point jumping into the water would be a bad idea.

It really just comes down to infrastructure. It’s possible to prepare for such events, but without large scale preparation they turn deadly.

Water conducts heat better than air. At exactly 36C wet bulb poeple would be running a fever but a large body of water would cool them better than air at 36C.

However, 100% humidity is rare it’s normal for the actual temperature to be higher than the wet bulb temperature. So local large bodies of water might actually be significantly higher than 36C at the time.

That's what I did when I lived without AC where it gets above 100F with high humidity. I would fill up the bathtub will cold water and cool off that way every few hours during the day when I was at home. I guess the water came from underground storage, it was plenty cold enough for that purpose.