As per your wiki link, it is about the extraction rate, which is not to be confused with how much oil there is - there will always be vast amounts of oil that's uneconomic to extract, or slow to extract, or both. The only "running out of oil" claimed by peak oil people is that we're running out of cheap oil.
They do claim the production rate will decline, and conventional crude has. The wells from this boom in the US have a production rate decline of 40% per year, so production is already declining nearly as fast as we can drill more and is predicted to peak soon.
Edit: Myself, I guess it's true that by throwing even more resources at oil (e.g. pursuing tight oil in other countries like in the US) we could still kick the peak down the road a little more and raise the production rate, but when the world economy can't afford such prices and the EROI is so poor then it seems more like playing word games than an honest rebuttle of the implications of peak oil.
They do claim the production rate will decline, and conventional crude has. The wells from this boom in the US have a production rate decline of 40% per year, so production is already declining nearly as fast as we can drill more and is predicted to peak soon.
Edit: Myself, I guess it's true that by throwing even more resources at oil (e.g. pursuing tight oil in other countries like in the US) we could still kick the peak down the road a little more and raise the production rate, but when the world economy can't afford such prices and the EROI is so poor then it seems more like playing word games than an honest rebuttle of the implications of peak oil.