he tried to stop the immigrant from mentioning her name and illegal status, then he was told by the immigrant that it is OK in the US, she won't be in any trouble. As a matter of fact in California there is law in place to guarantee that illegals won't be bothered by police.
A lot of illegals had to use somebody else's SSN to work, and that is never considered a problem because that is the only way for them to work legally. (while you will be in trouble if you have legal status or are legal to work but impersonate someone else)