I suppose the knee-jerk reaction is that if oil is pumped from US territory, it is US oil. It belongs to us and can be immediately subtracted from what we buy overseas. This may even be true in practice most of the time, since oil pumped in Louisiana or Texas can be refined and sold in Florida cheaper than oil brought in by tanker around the Horn from Kuwait.
The same can be said about crude produced locally by a US company, this especially holds for times when the oil market is stable. But when it is not in equilibrium and there are erratic swings in production or consumption, oil will react like any commodity. It will go to the highest bidder until prices stabilize at some higher level, regardless of where it is produced, or who is selling it. The only exception I can think of is in the event the government intervenes, and either nationalizes the oil industry or forces it to sell it here at a price lower than they can get for it overseas. I can only see this done in time of war, or perhaps as a public relations move by the producer to keep the local consumers from rioting in the streets. In general, the market, not geography, ownership, or national borders will determine the price.
And just what do we mean by "a US company", anyway? The stock is dispersed among companies whose stock is dispersed among companies whose stock is dispersed...ad infinitim.
Corporate collectivism, not only do we not know who owns what, nobody really cares.
I'm not sure I agree with you about the jobs issue, though. Even if what you say is true about most oil workers being foreigners, much of the support infrastructure along the littoral and deep in the heartland, supporting the rigs will employ Americans. Some of that bonanza will trickle down to us.