PolitiFact quotes Hinojosa:
"A large majority of the Republican Party believes that this man is a Muslim and was born in a foreign country, was not born in the United States," he said at the Central Texas Democratic Forum on April 24, 2012.
Hinojosa may have intended to say that a majority of Republicans believe both (and not or) propositions. In other words, the exact same group in the sample supposedly holds both beliefs.
For example (figures simply for the sake of argument):
52 percent believe Obama is a Muslim and born outside U.S.
8 percent believe Obama is a Muslim, but born inside U.S.
11 percent believe Obama is not a Muslim but was born outside U.S.
(71 percent believe Obama is a Muslim or born outside U.S.)
Consistent with PolitiFact's statement of principles, the fact check should have considered the less charitable interpretation. It is the best practice to inform the reader when one is using the principle of charitable interpretation in a fact check.
In this case, contrary to PolitiFact's principles, words weren't important. Hinojosa's specific wording was forgiven without comment in favor of a less literal interpretation.