It's.... somewhat naive IMHO (understatement). OK, downright wrong.
Oil prices aren't going to come down because we all boycott ESSO. The big oil companies don't set international oil prices, or production limits.
It's supply vs. demand, and the amount of oil wanted around the world is getting pretty close to the amount capable of being supplied. This was being pointed out a few months ago, as the OPEC ministers were agreeing to boost world production, and the Economist was warning that until the increased production came on-stream, that prices would be high.
Now, you might argue that fuel duty could be reduced, but that has absolutely zero, nada, zilch to do with OPEC or BP or ESSO.
Personally? I think the author either hasn't got a clue, or it's a deliberate attempt at propaganda from someone with an axe to grind. If the latter (my bet), you can take your pick as to their motives (blame the cartels / oil companies / globalisation / lizards dressed in people suits / UN / secret world governments / how big a chain letter can I create, and will it make the national news and boost my ego).