I have argued thus far that (ignoring foreign taxes and the possibility that a US tax would drive Sue out of the US) the US should tax Sue on her foreign surgeries. Even under the assumptions thus far, however, the analysis is incomplete. I must address the argument that we should not tax Sue as that would undermine her competitiveness.
The competitiveness argument is that, if Sue is taxed, she is handicapped in competing with foreign doctors who would not have to pay income tax on the same surgeries. It is not clear that Sue's competitiveness, in this sense, is in the best interests of the US. This would be true only if total US welfare is higher if the US does not tax Sue than if she is taxed. This could be the case, say, if the taxes would drive Sue out of business altogether, which does not seem likely. More likely, the benefits to America of Sue paying her fair share of taxes outweigh any marginal burden on her. But, this is a very difficult question which I cannot answer with any authority.
While it is hard to decide if we want to make Sue competitive, it is important to note a more straightforward defect in the competitiveness argument: Taxing Sue probably does not make her less competitive. If Sue is paid the same amount for foreign surgeries as she would in the US, not taxing the foreign surgeries just would encourage her to ply her trade offshore. She is less competitive only if the foreign surgeries pay proportionately less due to the lack of foreign income taxes on other doctors who would perform the surgeries. (The foreign surgeries may pay less, for example, because of more limited malpractice liability, but that is not a tax concern.) While possible, this seems sufficiently unlikely that the entire competitiveness argument seems questionable.
Tomorrow: Those pesky European taxes.