Think about it........if it were truly "bad gas" causing the problem, the shaking and poor running and the light wouldn't goout after it warms up..........since the gas is still being used but the engine smooths out as it warms, it's certainly not the gas. More likely some sensor going bad, like maybe an O2 sensor, and the engine's trying to either run too lean or too rich when cold. It warms up, the sensor finally gets normal readings. Probably something else, but along those lines.
Also, don't you think it's odd that while not everyone in Arizona buys only Shell or Chevron gas, yet they seem to have cars that run quite fine on the other brands? If all your other brands of gas were that poor, your roadsides would be littered with dead or dying cars.
Run from that dealer as fast as you can. All they want to do is open your wallet and checkbook and empty both.....to do nothign other than maybe replace some plugs, a sensor, a bad spark plug wire, or somethign equally simple. The rest of the $00 charge will be wall labor......that's the labor done to the car as it sits parked next to the back wall on the dealership.
ps........dealers do a lot of wall tuneups, too. Damned expensive considering how much work actually is done.