That's not true.
If he's giving up permanent resident status in the US, he needs to return his green card, along with form I-407 -- otherwise he will run into trouble. Maybe not immediately, but certainly eventually. We once wound up behind a couple in Dublin who hadn't properly surrendered the green card, and they were hauled off to the Frightening Little Room (as were we) so I had a good earful -- it was not pleasant.