A square foot is bigger than the area used by a person standing and people mostly weigh more than 40 pounds so that seems unlikely to be the design criteria for places people walk.
You're confusing the concept of concentrated load and the uniform load for a floor or room. See page 7 of the HUD guide [1], but local building codes may be stricter. Materials like floor boards must be able to support 250-300 lbs in the center between supports, but that's very different from a whole floor supporting 250 psf.
If you manage to squeeze 400 people weighing an average 150 lbs each into the average 400 sq ft apartment room, it will probably suffer structural damage unless it's a on a solid ground floor. That's one of the factors that goes into calculating the room and building "occupancy limit" signs you see in public places.
