He could be illegal, but the article states that he is a Texas man and his last name is Rodriquez, which is 4th most common surname in Texas.
"He did not have a valid license and was identified by law enforcement via a passport, police said."
Less than 2% of all American citizens in Texas even possess a passport. Only 0.2% of them routinely carry it around with them. And only 0.02% of all American Lamborghini-owners in Texas routinely carry a passport around with them. So the deduction that he is probably an illegal is quite valid.
Regards,