“Peak Oil” supposes a fixed amount of oil, which negates your statement.
However there are plenty of studies that disprove “peak oil supply” and highlight that oil is most likely a regenerative resource and not a finite source from dinosaur carcasses.
Then “Peak Oil” is, as you suggest, based on a false premise.
Still, even if the amount was fixed, some extraction is more difficult (expensive) than others, and will not be extracted until the price is high enough. This is the economics analysis of the situation.
So, Peak Oil is a doublefold myth.
The actual theory is better called Peak Cheap Oil. As many point out on every Peak Oil thread, we will never run out of oil. But production of cheap oil can certainly peak, and apparently already has.