If a house in town the 1910's or 20's had only an outhouse, does that
mean that it did't have running water inside the house?

Specifically, I mean Indianapolis. About a mile or mile and a half
south of the center of town. (Which was or at least became the poor
side of town, compared to the north side.)

My mother told me that she used an outhouse when she was little, but I
guess I assumed my grandparents still had a sink in the kitchen with
city water, rather than going out to a well, or pumping in the
kitchen.

What say ye?