According to the Original Peak Oil theory, the world ran out of oil in 1975
That would be the USA domestic and would be peak rather than running out.
Actually, King Hubbert, the person host associated with the term "peak oil" in the late 1950s predicted a peak in the U.S circa 1970 ... about when it happened. His prediction for a world peak was circa 2000, but he hedged that one with the recognition that massive new discoveries could push the world peak back a little.
If what we are seeing is the peak, it was the 1970s oil shock not the massive new discoveries that pushed the world peak back a decade.
BTW, Hubbert believed passionately in energy alternatives including nuclear fission. He wasn't a world is ending tomorrow doomer. He was a geologist who knew how oil production peaks and declines on a field by field basis, and since aggregate production is a function of the production of individual fields knew that somewhere down the road peak oil would happen.