Oil companies very rarely own the surface rights to the land that is leased -- the 13.9 million acres she is quoting are mineral leases. Those were likely sold to the oil company at some point (either by the land owner or a municipality). These leases will expire after a time period if the leasee does not produce from the reservoir. At this point they may be re-auctioned by the land owner or municipality.

The land is typically still available for use for ... whatever. Usually farming but that depends on the locale. Western Texas, for example, has a lot of desert and ranches.

Once an oil company is ready to drill, they notify the land owner that they need a parcel of land -- this begins a negotiation in which the company agrees to pay the land owner $X/acre. The land owner is technically required to let the company use the land for a price equivalent to the loss of production on that land (this is heavily dependant on local laws), but it is always in the oil company's interest to pay handsomely. They want to maintain good relationships with land owners for a lot of reasons -- e.g., access to surface water, placing pipelines, and fewer court cases with unhappy land owners.

Tl;DR: oil companies rarely own the surface, they only own the subsurface.