As others have already pointed out, this bogus plan has been floating around for a long time, and it is still just as useful as that "floater" in your crapper.
If all customers leave Exxon-Mobil, it increases the demand for other brands. When demand goes up, price goes up. What this plan does is raise the prices for Shell, Union, BP, and all other brands. When the demand for Exxon-Mobil goes down, the price will come down until demand goes back up. So if everyone else will agree to pay higher prices at other retailers, I will enjoy low prices (and short lines) at the local Exxon-Mobil station.
Actually, the price of fuel isn't going up. It fluctuates, like all other commodities, but the real price has come down over the years. The problem is the "price" (value) of a dollar bill has gone down farther and faster. The price of fuel is no different the prices of milk, nails, and light bulbs in this regard.