That is a reason for scepticism, but not a proof that current claims are false. Most of the arguments depend either on estimates of how much oil there is and what it costs to get at it or on estimates of the cost of alternatives, such as tar sands, liquified coal, solar or nuclear power. Since I am neither a geologist nor an engineer, I prefer to look at what economics can tell us about the situation.
The economics of depletable resources was worked out by Harold Hotelling more than seventy years ago, although outside of the economics profession almost nobody seems familiar with it. The argument is straightforward. Owners of oil underground can choose when to pump and sell it. If the price of oil is rising fast enough so that oil in the ground pays a higher return than money above ground, it pays to leave the oil in the ground—postpone production in order to get a higher price in the future. That reduces present supply, shifting the present price up, increases future supply, shifting the future price down. In a world of secure property rights and perfect information, the process continues until the projected price of oil, net of pumping costs, is rising at exactly the market interest rate, forever. Any faster than that and people shift production to later dates, any slower and they shift it to earlier dates. Unless the people who control the oil and decide when to pump it are wildly off in their predictions of future prices—the theoretical analysis assumed perfect information—the usual crisis scenarios can't happen.
There is, however, a second critical assumption—secure property rights. Suppose I own underground oil, but I believe there is a substantial chance, say ten percent each year, that someone else will seize control over it. I will only leave the oil in the ground if the expected rise in oil prices is enough to compensate me not only for the interest I could have earned on the money I would get by selling the oil now but also for the risk of losing the oil. So insecure property rights result in producing more oil now, less later, and a price pattern that rises faster than in the Hotelling model.
Essentially all property rights in underground oil are insecure. It has surely occurred to the current rulers of Kuwait and Saudi Arabia that money in a Swiss bank account is a safer asset than oil under the desert. The government of Norway is unlikely to fall to a coup or an invasion—but the politicians who control it today cannot be confident of controlling it ten years from now, so have an incentive to pump now and use the money to maintain their political power.
In some countries, such as the U.S., much of the oil is owned by private firms, not governments. But their property rights too are insecure. As we have seen in the past, a rising price of oil results in political pressure for price controls, "excess profits" taxes, and other forms of more or less disguised partial expropriation.
The implication is straightforward. The arguments about oil geology and the cost of alternatives may or may not be correct—on the basis of past evidence, the claim that we will shortly run out of oil should be viewed with considerable scepticism. But the economic argument implies that owners of underground oil will tend to pump and sell earlier than they would in a perfectly functioning market, and hence that oil prices will raise faster than the simple version of the economic argument predicts. How much faster depends on how insecure the relevant property rights are.
There is one further complication whose analysis I leave as an exercise for the readers. Insecure property rights have a second effect—they make finding oil less profitable, since after you find it someone else may steal it.