Obviously oil has a fixed supply... there is by definition only a finite amount of it, given that we live on a spheroid with a finite volume out of which to extract it. Supply doesn't grow with demand, as that would imply new oil is somehow being created with demand and that, given infinite demand, there would also be infinite supply.
What does grow with demand is technological innovation and effort, and while we were not as close to the actual limit as we assumed with "peak oil", that doesn't mean the limit itself was fictional.
>As long as someone is willing to pay for it, it will be provided. And even cheaply
This is only true until it isn't. At some point oil will become economically and technologically infeasible and alternatives will win out, because no one wants the million-dollar a barrel oil economy that results when we have to resort to mining Titan for it.