If someone walked into your business to fill a slot that required certain credentials, would the burden fall on you to prove that he didn't have such credentials? If he claimed to have such credentials but later serious doubt was raised about whether he told the truth, whose responsibility would it be to clear things up?
It's nonsense to say that anyone but Obama has the burden of proof in this case.
In the minds of those doing the “hiring,” they ALREADY HIRED THE GUY. Now you are viewed as the ICE officials coming in saying, “He doesn’t have the papers!” This insults you, cause you just hired the guy, so now you are even more determined to protect him.