Agreed. You will need it when sleeping in a hotel, hostel, boat, etc. and when traveling out of town by bus, train, etc.
There aren't many occasions when you'll need it around Hanoi. It's good to have a couple photocopies made of your passport data and current visa, as landlords and travel agents need them from time to time.
When I was living abroad, we would also need it when entering a internet cafe. Once a Vietnamese guy lost his passport twice at a Carrefour's internet cafe. Coincidentally, another Vietnamese guy got it for both times. And after the second time getting back his PASS, the PASS-loser gave a banquet for the whole Vietnamese students in the city.
The consequences of losing PASS is awful, you have to wait for a long time and spend an amount of money to remake it, and maybe some bad guys in the 80 million-people country of Vietnam will use it to do something really bad, who knows?