I was once flying SK from MXP to CPH. I got to the airport way too early - unfortunately having a dirt cheap restricted ticket I could not get on an earlier flight. Anyway the check-in agent refused to check me in 4 hours before departure as "there's an earlier SK flight to Copenhagen and your luggage will get loaded in that flight instead of the one you are booked on"... that was interesting - I thought that security regulations explicitly make it very difficult for this kind of things to happen.
In the end I had to hang around a few hours before the earlier flight departed and she was happy to check me in.
It looks like the incompetence is not limited to just customer service agents then.