"No human is illegal" indeed. Their actions, however, may well be. In the case of his parents, they acted against the law when they entered and remained in the United States without going through the proper channels. More illegal acts were commited by obtaining false or forged goverment documents, which may or may not have been accompanied by evasion of federal taxes. Lying about your immigration status for the purposes of employment is also an illegal act.
No, no human is illegal. But these particular humans, by the wieght of their numerous illegal acts, do sound a bit like criminals.