Scott, I see your point now, and understand where the confusion comes in. Let me explain the curves you saw in this page:

The demand curve is trending downwards because the higher the price, the less the consumer will demand.
The supply curve is trending upwards because the higher the price, the more producer will supply the good to the market.
In short, these curves show the "response" of buyer and seller due to the change in price of a particular product. So the curves depicted a "price-driven" behaviour.
Now the shape of the two curves you saw in that picture is applicable in a fully competitive market where the supplier can enter the market and cope with the demand instantly. In reality, the gas market is not as responsive, i.e. when demands goes up, the sellers are not able (or they don't want to) to increase their production to cope with the demand. So in such a market where the supply is very rigid and non-responsive, the supply curve is almost "VERTICAL"

see this 2nd diagram here:

So when people say "demand has increased", there're two ways to explain it (and they mean different things):
(1)If the demand increases because the price is lower - for example the demand increases for iPhone because Apple slashes price, then the demand is in response to the price change and you are moving down the demand curve.
(2)If the demand increases, because more people need it, e.g. outbreak of disease, people need one particular medicine to cure, then you are SHIFTING the whole demand curve upward and to the right. (exactly opposite to what the 2nd diagram above shown, i.e. instead of shifting from D1 to D2, it shifts from D2 to D1). And if the original price of goods is at P2, shifting the demand curves up will move the intersection to P1, i.e. resulting in higher price.
There's nothing wrong with the law of supply and demand, the theory has existed since human started trading with each other. It doesn't matter what kind of market you're in, be it a monopoly, oligopoly, monopolistic, perfect competition or etc etc... it's all "supply and demand". Whatever factors you guys were talking about, e.g. "sellers price-fixing, OPEC quota, different people have different perceived values of what a particular good is worth, and etc etc...", they all go into affecting the supply/demand curves (you can move up or down the curves, or you can shift the curves to different locations entirely). At the end, the price is determined by the intersection of the two curves.
In short, everything is driven by supply and demand. If you disagree that's because your assumption of the "supply and demand" theory is different from those who developed and taught such theories at college.

Sorry..I am in guilt of jumping off the topic too much. The virtue of having a PhD degree in applied economics means that I am 'naturally' attracted to such discussion. I shall stick to audio from now on.

Hang on for a second. Now I might have the wrong perception of the law of supply and demand. Isn't it (essentially) "as demand goes up, the price comes down"?