Peak oil said we'd run out of oil Real Soon Now, full stop

Peak oil refers to the moment when the production of oil has reached a maximum and after which it declines. It doesn't say that we'll run out of it soon, just that production will slow down. If consumption increases at the same time, it'll lead to scarcity.

If you are trying to rebuild you don't need much oil

Well, that probably depends on how much damage has been done. If civilization literally had to be rebuilt from scratch, I'd wager that a very significant portion of that cheap oil would have to be used.