Paper tickets are a lot more common than you probably think... A lot of airlines simply don't have interline e-ticket agreements (ever flown an HP-operated flight on UA ticket stock? ), and when you're flying on two airlines that can't see into each other's reservations system, they really do make life easier.

That being said... I think the biggest problem with paper tickets is improper training, and you're right that mistakes are more common--I once had a boarding pass reissued and the agent (UA) threw away the flight coupon that was stapled to the original BP.

The bottom line though is that if you complain, UA will probably back up its agents based on your description of what happened. It's an easy slip-up, but your friends probably should have been more careful with the flight coupon--there's not a lot the UA agents could have done at that point, and $200 isn't a huge sum to pay in the grand scheme of things.