Nowhere in the article does he "concede he came to the U.S. illegally."
There is no US visa that allows living there for 20 years without work authorization. He entered illegally (or overstayed illegally) then tried to adjust status based on marriage, which is fraud.
That may sound like a distinction without a difference to you, but legally they provide very different avenues for acquiring a residency permit.
We also now know a judge refused his Habeas corpus petition, and he has a final order of removal -- signed by a judge, not an administrator.
He also refused to be deported to Ireland.