Did you read the text I bolded in your citation? Or did it have too many hard words?
No need to be a smartass, Poohbah. I've endevoured to be polite and civil in this discussion, and I'd appreciate the same from you.
The bolded text you posted has to do with a specific situation involving a nonresident alien and exemptions they have from certain tax considerations if none of their income derived from sources within the US.
It does not state that only nonresident aliens should use Section 861 to determine sources of income.
On the other hand, the instruction manual for the Code, the regulations, state that Section 861 and following determine the sources of income for the purposes of the income tax, without any qualification either in the regulations or the code as to alien/citizen/resident/nonresident.