this is a shockingly ignorant interpretation. They're not exporting more fuel to create an "artificial shortage"; oil is priced on the world market, and the US imports most of its oil. (Note that it wouldn't necessarily be any cheaper if it weren't exported; they'd just scale back refinery output. Fuel delivery is on a just-in-time basis; they don't keep stockpiles of the stuff in tankers.)
The wholesale, untaxed cost of one gallon of unleaded is about the same in the US and the EU and everywhere that isn't a net oil exporter with a heavily subsidised national oil company. The "oil price" quoted in US financial news is inaccurate, because it's NYMEX crude, which is not the global benchmark; the global benchmark is Brent, which is trading at about $25 a barrel higher than WTI. Oil companies are exporting diesel fuel because there's a demand for it outside the US and the US has the refinery capacity to process it; the combination of increased fuel economy standards and higher fuel prices changing travel patterns have led to a c. 3 million barrel a day fall from peak consumption in the US.
Americans already pay lower prices for fuel than anyone in the developed world. "Hurting the economy"? Taken a look at how the global economy is doing? Not that good anywhere; part of the problem is that economic recovery leads to oil supply constraints and pushes prices inexorably upwards. One of the major and largely unacknowledged factors of the 2008 economic collapse was high oil prices due to the fact that the world market was using pretty much every barrel of oil produced, and there was very little to no slack or production overhead in the system.