The Washington Post article (or actually the Associated Press article) refers to The New England Historic Genealogical Society, and the original article can be find at its website Americanancestors.org with the subject title NEHGS Discovers American Kinships of Prince William's fiancée. Kate Middleton's American Connections include President, General.
Included in the article is also a link to a chart (pdf) showing the degree of relationship Miss Kate Middleton has with President George Washington and others. Unfortunately the article doesn't tell exactly how Kate is related to the said US notabilities and no references to sources are stated, which would have made the article more interesting.
The NEHGS researchers behind the discovery include the well-known genealogist Gary Boyd Roberts, who is the author of several books including Ancestors of American Presidents. His website can be found here. This gives in my opinion the information more credibility, but still it would be interesting to get more details.
I have earlier mentioned (1 and 2) William A. Reitwiesner's website Wargs.com, which includes among others Kate Middleton's ancestry table. I should have mentioned, however, that Reitwiesner did the work together with the British genealogist Michael J. Wood.
