No, this is incorrect. Oil prices are set on a global level. The only differences in the end gasoline price are due to:
1) taxes on gas
2) distance it has to be transported
The oil companies all essentially sell oil based on the futures market. They set contracts and then deliver on those contracts.
Also, you and Nigel are both wrong. They neither want oil cheap, nor do they want it too expensive.
Too cheap and they do not recover production costs.
Too expensive and they risk demand destruction and increased economic viability of alternatives.
Oil companies want to stay around fair value and keep it as stable as possible. Currently fair value is in the $75-80brl range. It is currently being driven up due to instability in Mid East.
You left out refinery capacity.
And, while I agree that oil companies don't want too high prices for too long, they are perfectly content with short-term supply shocks every now and again driving the price up. And because demand for oil is fairly inelastic until you get around $4.00 average for gasoline (like we had Summer '08, and i'm talking national average, not CA) because there are few alternatives.