Here's how the argument goes. From quantum mechanics, we get the uncertainty relation
$$\Delta E \Delta t \geq \hbar,$$
where $\Delta E$ is the uncertainty -- or statistical spread -- of the energy, and $\Delta t$ is the uncertainty of the time.
Following this, physicists reinterpret the uncertainty $\Delta E$. Rather than representing a quantification of our lack of knowledge about the energy of a system, this is interpreted as being, somehow, the amount of "free" energy that a system can borrow in violation of the First Law of Thermodynamics. So if we have mean energy $E$ and uncertainty $\Delta E$, it means we "actually have" energy $E$, and then Nature gracefully lends us $\Delta E$ to overcome some energy barrier, which we quickly repay in time $\Delta t$.
However, that puts us at
$$\Delta E \geq \hbar/\Delta t$$
which puts no limitation how much energy we can borrow. Or, rather, it puts a lower bound; we must borrow at least $\hbar/\Delta t$ worth of energy. Or, we could borrow even more! If this is true, then we have infinite energy forever!
The oil companies will go bankrupt!
The oil companies will go bankrupt!