According to the U.S. Energy Information Administration, you are correct in that very little fossil fuel is used in electrical energy production [1]. However, quite a lot of natural gas is used, which is what the GP was describing, so I think his question is still quite relevant.

[1]: https://www.eia.gov/energyexplained/images/charts/consumptio...

but the grid does use natural gas for peaker plants to respond to demand changes.

Natural gas comes from oil wells. If demand for oil reduces, and wells close, natural gas production will decline too.

While Natural Gas was considered a byproduct in earlier times when it couldn't be harvested efficiently (and had to be "flared"), current technology does allow us to do so, and wells targeting gas specifically are not uncommon.