And as I mentioned above, the regulations say that "Sections 861(b) and 863(a) state in general terms how to determine taxable income of a taxpayer from sources within the United States" [in 26 CFR §1.861-8(a)(1)], and "The taxpayer's taxable income from sources within or without the United States will be determined under the rules of Secs. 1.861-8 through 1.861-14T for determining taxable income from sources within the United States." [in 26 CFR §1.863-1(c)]
Furhthermore, the tax code jargon for your "non-US citizens living outside the United States" phrase is "nonresident alien individuals," and 26 CFR § 1.1-1(b), to which you refer, says that for these people, you should "see sections 871 and 877," not §861 as you suggest.
I guess I still don't follow your reasoning - I apologize. Could you please refer me to where the law or regulations say that §861 only applies to the income of nonresident alien individuals? I'd really like to know.