The Emoluments Clause not only states “… without the consent of Congress…”, but it also states that these prohibited appointments are “…from any King, Prince, or foreign State.” Keyword: foreign.

First, Hillary (if she is chosen) will be confirmed by Congress, as are ALL Cabinet appointees, per Article II, Section 2.

Secondly, for purposes of the Emoluments Clause, “a ‘foreign state’ is deemed to include an international organization in which the United States is NOT a member.”
Source: http://micronations.wikia.com/wiki/Emoluments_clause

It was unanimously added to the Constitution to prevent international conflicts of interest, and to prevent the establishment of a “special” Civil position which would be created just to place a presidential appointee.