You were misinformed. The residential meters turn at the same rate 24/7. Power companies make a better margin at night when the smaller less efficient plants can be pulled offline and their staffs trimmed, so that's when they want more residential usage.
Large-scale industrial operations can squeeze out better rates by sifting their operations to off-peak hours. The spend enough millions to get someone's attention. But residential customers pay a fixed rate per KWH, regardless of at what H of the D.
My usual pattern is to pump in a lot of cool night air, and to sleep under blankets. That cool air lingers in the house, and the AC only kicks in during the heat of the day. I pay the same for energy at peak and off-peak hours. But by keeping it cool inside when it's cool outside, and then maintaining the cool inside when it's hot outside, I'm using less and paying less for it.