Rephrase the question more like: "How is the US Congress able to tax incomes earned by American citizens/companies in France?" If China (the government) were t

Rephrase the question more like: "How is the US Congress able to tax incomes earned by American citizens/companies in France?" If China (the government) were to go into space and start mining things, the US would likely be limited to diplomatic recourse, or if objectionable enough, perhaps war. Clearly, American government does not directly control Chinese government, but does have influence over it. If a Chinese mining company (not the government) goes into space and starts mining, the American government's course of action is likely limited to pleading with the Chinese government to restrict their mining companies from being able to do so, using the aforementioned diplomatic measures as bargaining chips in the negotiation. If however, an American mining company wants to go mine an asteroid, the US government is assuming a total control / responsibility of their actions, even while those actions are not on US soil, or even on any terran soil whatsoever. Because the US government believes it controls all US companies to the extent that they do, they believe that they could forbid an American company from mining resources not in America, or in this case, not even on Earth. This assertion is them saying that they either don't care if mining companies mine asteroids and other planets, or that they might actually acknowledge that they don't have the power to forbid it. I haven't been following it closely enough to say which kind of concession it is.