Tina Turner turning in her U.S. citizenship

Does the below paragraph mean that any "former" American who becomes a citizen of another country will STILL have to pay taxes to the U.S. government? How does that work?????  Are they saying this to scare her or is the government now going to start taxing every former American who renounced their citizenship?

BTW, in reading another article on the same subject, the top tax rate in Switzerland is 22.4%. 

"But if the 73-year-old singer is making the move to cut her tax bills, she will probably never admit it. The U.S. government warned Americans 'Renunciation of U.S. citizenship may have no affect whatsoever on his or her U.S. tax obligations (my emphasis).

She’s an American icon, but Tina Turner is reportedly about to renounce her U.S. citizenship in order to become a Swiss citizen.

The “Private Dancer” singer has lived in the Zurich suburb of Kuesnacht since the mid-1990s. The Zuerichsee-Zeitung newspaper said on its website that the local council announced its decision to grant the 73-year-old Turner citizenship in an official notice published in today’s edition, according to The Associated Press.

The decision still requires formal approval from state and federal authorities.

Turner’s rep did not respond immediately to ABCNews.com’s request for comment, but she told Zuerichsee-Zeitung that the singer wanted to “clarify her situation.”

“Tina Turner will therefore also give back her U.S. citizenship,” her rep told the Swiss newspaper.

http://abcnews.go.com/blogs/entertainment/2013/01/tina-turner-to-become-swiss-citizen/