Can one half tank of "bad gas" cause a 2003 Corolla to vibrate violently on braking and acceleration

That is what the Toyota service center is saying caused a sudden problem with my car. I am skeptical that they are saying this just to avoid paying the repairs because the car is under warranty. They say they need to drain the tank, clean the tank and the inputs completely and I need all new sparkplugs and it will cost almost $800 and it is excluded from warranty because the "bad gas" is not their fault. I am suspicious because I buy my gas only at Mobil and I usually buy a half tank at a time and keep the tank close to full, so the gas in my tank is always a blend of one purchase and another. Also, I read that bad gas can cause a problem over time with sputtering, NOT sudden bad shaking vibrations. Can anybody advise me on this? Thanks