Not exactly the most honest of sources there, and as usual it looks like they're trying to mislead the sheeple. In this case, they're counting on the fact that most of their readers don't know how criminal jurisdiction and immigration law work in the United States. I also expect that they are using a misleading definition of 'illegal immigrant'.
Consider the following scenario:
Juan, a Mexican national, crosses the border in Tijuana. He tells ICE that he is visiting the United States to attend his god-daughter's graduation, and he will be going home next week. His luggage contains a graduation present, several changes of clothes, and a tourist's guide to Los Angeles (Spanish edition.). ICE waves him through. He is legally present in the United States.
Dio, a Mexican national, crosses the border right behind Juan. He tells ICE that he is visiting the US to see his ailing mother (a legal resident) one last time. His luggage contains several changes of clothes, an unregistered pistol, and three kilograms of cocaine meant for resale. His mother is in perfect health, lives in Guadalajara, and has instructed him never to darken her doorstep again after what he did to that poor man in 2004.
As Dio has lied about the purpose of his visit to the US, his permission is legally void. When he gets caught trying to sell the drugs, his paperwork is updated to reflect that. He is an alien illegally present in the United States. As he crossed a national border, his crime is under Federal jurisdiction. He will be serving time in Federal, not State, prison.