It must be the impression the show gives people. I am not a viewer, but my father in law said the same thing. Basically, according to the show, if they can't prove someone is from a country, they can't force a country to take them back, so they release them. My father in law is a pretty regular viewer, so it definitely isn't a fluke thing.
I've seen the show once, and the woman without a passport had admitted to the officers she was from Ukraine. She was detained because of that admission and others, but was finally able to go back to Ukraine faster than she would have otherwise because someone dropped off her passport.
So the show is definitely giving two messages to its viewers.