"That is because these systems use the central power grid, which largely runs on fossil fuels, as a kind of battery to cope with power shortages." - not according to PG&E reports from Sonoma County, California, where less than 5% is fossil (natural gas) for 2022.
PG&E Generation Mix: 5% Biomass & Biowaste, 1% Geothermal, 2% Eligible Hydroelectric, 22% Solar, 9% Wind, 8% Large Hydroelectric, 5% Natural Gas, 49% Nuclear.