There doesn't appear to be any question that some fields can refill themselves, and that basement rock oil exists in large quantities in some places, but the jury is still out on where the oil comes from. I just can't wait until we can get that pipeline built and tap into the Caspian Sea region so we can quit making the Arabs so rich.
It's counterintuitive, though. Basement rocks here in North America are pre-Cambrian granite. It not only couldn't serve as a source rock, but it has no porosity or permeability. In lay terms, no oil could flow through the rock if it wanted to. It would make an excellent seal.
The only way it could produce is through heavy fracturing and with a source below it. We see that all the time in the overthrust belt of the Rocky Mountains. But there, the "basement rocks" aren't really basement. They have been overthrust onto younger rocks which are providing the actual source of the hydrocarbons.
Whether that's what is happening in central asia, I simply couldn't say.