You must have missed this part.
the link...
"But local officials, which issue birth certificates registered by the Texas Department of State Health Services Vital Statistics Unit, told the women they would no longer accept either the matricula consular, which is a photo ID issued by the Mexican Consulate to Mexican nationals living in the U.S., or a foreign passport without a current U.S. visa. Undocumented Central American women are also being turned away because they only have a passport without a U.S. visa. “They are locking out a huge chunk of the undocumented immigrant community,” says Harbury"
Guess you need a visa. If you're an illegal you won't have one.