But the trust issue was mentioned specific to illegal immigrants - or, undocumented immigrants as I also prefer.

People marry other people "for" something all the time - for their money, for their looks, for children, for status, for their race..... You're always going to have to make sure that the person is sincere.

Not "trusting" someone implies that a person is dishonest or underhanded. I don't think that someone who enters a country without papers is automatically a dishonest or untrustworthy person.
Get used to me. Black, confident, cocky; my name, not yours; my religion, not yours; my goals, my own; get used to me. -Muhammad Ali