Actually, it doesn't. Not if it is followed. At IV, Sec. 2 and the 14th amendment define citizen of the US, and Mr. and Mrs. Bomber can only birth naturalized citizens abroad, and that by grant of Congress, not by the constitution alone.
Obama is claimed to have been birthed in Hawaii. There is an argument that he is not NBC, I think a good argument - but it is a different argument than the one that works for Mr. Cruz, who openly admits being born abroad.
If Obama was born abroad, he is not a citizen at all. Not by operation of the constitution, and not by Act of Congress.
Your argument here would deny citizenship of John McCain (born in Panama) and of Lowell P. Weicker, Jr., (born in Paris) and the late George Romney, born in Mexico of parents who had been citizens of Utah Territory before statehood and fled to Mexico in a snit over Congress requiring anti-polygamy laws as a condition of Utah statehood and forming a Mormon colony in Mexico with no evident intention of ever returning to Utah or any American jurisdiction.
Personally, I hate Weicker more than I hate Obozo but the mere fact that his parents were in Paris on business for Squibb Pharmaceutical when he was born in about 1930 did not render him ineligible as a non-NBC, much less being thereby rendered "not a citizen at all."