Back to my Sue hypothetical from yesterday. The right would say that we can't tax her, so we shouldn't. I prefer a more optimistic, can-do, American approach: See if we want to tax her and how, and then figure out a way to do it. (In other words, I'm putting off discussing the hard practical problems.) Also, let's ignore the European taxes for now.
So, should the US tax Sue on the income received as a consequence of her offshore surgeries? Well, she is a US citizen. The historic US view has been that US citizenship alone justifies taxation on world-wide income. After all, Teddy Roosevelt would send gunboats to protect a US citizen. This argument just seems out or date to me, however.
Sue also is a US resident. One can argue that she gets all of the benefits of living in the US and should pay her fair share of the cost of our country. This argument, while having some force, does not seem powerful enough to justify full progressive taxation.
But, there are more reasons for the US to tax Sue. In the abstract, much of the money generated by the foreign surgeries was earned while she was in the US. Performing surgeries just finished a long process. She learned her art and honed her skills in the US. Without her US life, she could not have demanded megabucks offshore. The US supported her earning process by supporting her education and the schools and hospitals where she trained. Less importantly, she arranged and prepared for the offshore surgeries in the US. All of this convinces me that the US should tax her offshore surgeries. (Remember, I assumed away a bunch of hard issues above, for now.)
I suspect that unspoken analyses like that in the preceding paragraph is why most tax types accept residency as a basis for taxation. Current residency alone may not show large current governmental benefits, but may be a good proxy for lifetime benefits that provide a sound basis for taxation.
Law types, note that this analysis is somewhat inconsistent with legal (power) notions of jurisdiction. These notions would suggest that some of the foreign surgery earnings (some amount viewed as really earned offshore) are beyond US taxing jurisdiction. Ignoring physical notions of jurisdiction is acceptable here, however, because, as it turns out, income is a concept, not a thing, and doesn't really have a geographic source!
Have I convinced you? More tomorrow.