I think this shows that a good part of the price rise in from early 2007 was not just supply trying to keep up with demand, but speculation pushing the price up. Prices above $80 to $100/barrel were not justified.

I do not see the logic in this from a pure supply-demand perspective. As demand increases, the price goes up. This makes more supply viable. When supply finally meets demand, the price will be at its peak and the production will be at its peak. That these two did in fact line up supports a supply-demand argument.

Suppose that there was a change in demand in August (Chinese and Olympics). The demand would drop and that high cost supply would be pulled back off the market.

I'm not saying that speculation or the financial bubble didn't play some role, especially in paper prices. What I am saying is that the price and production data are consistent with the thesis that supply-demand played a significant role in the price run-up. Some sort of demand data (other than paper pricing) would need to be analyzed in order to show that this was not the case.

Ultimately this is all too complex for simple models to explain, but the simple models can help to gain insight into aspects of the situation. Unfortunately, humans can't handle complexity very well and thus become heavily vested in a simple model when the reality is otherwise. This leads to endless bickering over simple models, none of which are entirely correct.