I don’t think this is true in many areas. In our area, during the summer the neighborhood is running A/C when the sun is at its peak. During the winter, heating. Also the transport loss from a power station is nothing to sneeze at - my understanding is that locally produced power often just results in reduced demand on the larger grid.

Here in the Sierra foothills, it's been a blazing hot summer. About 90% of our PV generation powered our home air conditioning. We shipped very little energy to the grid on hot days. And it was awesome to have a comfortable environment without sucking grid power on the days when it hit 113°F.