If they were here illegally, there would be a paper trail. Just like the paper trail that was found in his mother became a citizen.
The absence of any evidence is pretty damning.
I assume that you meant, "If they were here legally, there would be a paper trail." With that said, I suggest you read the article. Although the title of the article implies through the use of a question that Curiel's parents are illegal aliens because they never became US citizens, this is pure crap because no law requires lawful permanent residents to become naturalized citizens. What raises the BS level even further is that the details in the article contradict the title and the lead paragraphs in that the article contains photos of Curiel's father's visa documents from 1923 and 1943 as well as his work permit. There apparently is a paper trail if you bother to read the article.