I believe she misspoke on the not part of America comment. The District of Columbia is a corporation, 10 miles square that "houses" the government of The United states of America. More accurately, she could have said that DC is not a state.
The "District Clause" in Article I, Section 8, Clause 17 of the U.S. Constitution states:
[The Congress shall have Power] To exercise exclusive legislation in all cases whatsoever, over such District (not exceeding ten miles square) as may, by cession of particular states, and the acceptance of Congress, become the seat of the government of the United States.
In 1790, the land on which the District is formed was ceded by Maryland following the passage of the Residence Act. Virginia also ceded land that helped form the District, but that land was returned to Virginia in 1847. The Congress did not officially move to the new federal capital until 1800. Shortly thereafter, the Congress passed the District of Columbia Organic Act of 1801 and incorporated the new federal District under its sole authority as permitted by the District Clause. Since the District of Columbia was no longer part of any state, the District's residents lost voting representation.
Voting rights of citizens in the District of Columbia differ from the rights of citizens in each of the 50 U.S. states. The United States Constitution grants each state voting representation in both houses of the United States Congress. As the U.S. capital, the District of Columbia is a special federal district, not a state, and therefore does not have voting representation in the Congress. The Constitution grants the Congress exclusive jurisdiction over the District in "all cases whatsoever."
In the United States House of Representatives, the District is represented by a delegate, who is not allowed to vote on the House floor but can vote on procedural matters and in congressional committees. D.C. residents have no representation in the United States Senate. The Twenty-third Amendment to the United States Constitution, adopted in 1961, entitles the District to three electoral votes in the election of the President and Vice President of the United States.
The District's lack of voting representation in Congress has been an issue since the capital's founding. Numerous proposals have been introduced to change this situation, including legislation and constitutional amendments, returning the District to the state of Maryland, and making the District into a new state. All proposals have been met with political or constitutional challenges and there has been no change in the District's representation in the Congress.