I don't know the specifics of the travel ban, but have heard about it here and there. Perhaps some of it is urban legend mixed with fact. However, in fact it is sort of mentioned in the article you cite
" If found ineligible for a visa or the VWPP to come to the U.S., a renunciant, under certain circumstances, could be permanently barred from entering the United States."
I think it applies in large part to tax dodgers, but may apply to others.
http://www.americanlaw.com/exclud10.html
It also is not looked favorably upon by visa-granting officers, who can be rather arbitrary in who gets a visa and who doesn't.
My point is you might want to check with someone more official than those of us on this board before doing so, if that is something you are considering...