See message 2 in http://flyertalk.com/forum/showthread.php?t=678150 for an example.

A friend told me another example; he arrived a little bit after the listed checkin time, and they would not let him check in, although he would have made it on the plane before the door closed if they did let him check in. However, not long afterward, I was on a flight on the same airline, the last passenger to board appeared to have just run through the terminal, telling her friend that it took only 10 minutes to get to the plane from her late arrival at the airport (flight was almost, but not quite, full).

Seems that the airline in question was lenient with checkin time in the case of a non-full flight, but strict in other cases. Could it be that the other cases involved overbooked flights, and the airline wanted a way of getting passengers off the flights without having to offer VDB or IDB compensation, or list an IDB on their record?