The source of the “3 days” number likely comes from an experiment two scientists did in 1944 where they ate only dry food for a period of time; one ended the experiment at 3 days in, and the other at 4 days in. However since they stopped the experiment before being in any real danger, the actual survival time at room temperature likely exceeds 3-4 days.
The average person could probably still be saved after 5 days without water or more.
3 minutes without air.
3 days without water.
3 weeks without food.
I think 3 days without water is too low but also heavily depends on your local climate.
https://en.m.wikipedia.org/wiki/Rule_of_threes_(survival)
So in order of importance, air, shelter, water, food.
In the section about water:
The average person could probably still be saved after 5 days without water or more.