Hi Garlan,
SolarCity is not passing on charges from local power providers. The homeowner is billed separately for that.
Here's a sample SolarCity residential PPA:
https://www.solarcity.com/sites/default/files/sc-contract-resi-ppa-2.9.pdf
SolarCity retains ownership of the PV system and the electricity generated. The homeowner pays nothing for the PV system - and instead agrees to pay for all electricity generated at the designated rates (for 20 years). SolarCity tracks how many kWh were generated each month by its PV system and bills the homeowner accordingly.
When I was shopping for my PV system, I opted to purchase outright. Sounds like you made the same decision for yours. While SolarCity will sell (or lease) PV systems to consumers, many opt for a PPA instead. In such cases, it seems pretty clear that SolarCity is a supplier of electricity - even though they don't fit the mold of your typical electrical utility (e.g. ComEd).