Sounds like by the time they got to the "right" check-in counter they were just past the check-in cut-off time, the employee checked with a manager to see if they could re-open the flight and the manager said no not for five people.

Guess they initially got in the domestic check-in line and then were redirected, although I'm having a hard time believing that both domestic and international check-in lines were ~40 minutes long.