...to interrogate any alien or person believed to be an alien as to his right to be or to remain in the United States.’
That is the line I am referring to. Such an approach is forbidden by the Arizona law. In order to "interrogate" a person in Arizona, that person must have committed a possible underlying offence first.
The federal law is much more broad than the Arizona law, and would have justified Obama's assertion that a man going out for ice cream with his child could be stopped and asked for papers. The federal law would allow that. Arizona's law would not.