That's true in a lot of places but not really in California, where there's a lot of customers for solar. I don't need to go into the reasons why. It's California.
Solar can also reduce grid costs, by e.g. shaving the yearly peak power demand, which is usually a summer afternoon so it's not clear cut.
Probably the bigger impact is bad incentives for the people building the grid, who are often able to do what they like and get a guaranteed percentage return on top, which pushes them to spend more than they need to. This has been particularly pronounced in Australia I believe.
