This is provably false. If oil couldn't be produced fast enough to meet demand, the price of oil would not be $110 a barrel, it would be $110+x per barrel, where x is the maximum number of dollars people are willing to pay to use the available supply of oil.

This thinking generally leads people to miss OP's point, which is that the world will never run out of oil. Price will always fluctuate to meet demand (so long as we let the market set the price).