I do sympathise with you as that is pretty awful Customer Service. Unfortunately KLM and Customer Service do not go together. I have only flown with them twice and pretty poor both times.
We were flying back from Zurich via AMS then home to ABZ. Our flight from AMS - ABZ was the last flight of the night 20.20. We arrived at Zurich at noon, to be told at check in that we couldn't check in for AMS-ABZ as there was only one seat left (we had these flights booked for 8 months!!) The girl at ZRH said there was nothing more she could do and we would have to wait until we got to AMS and go to the transfer desk. So we had a very stressful flight, not knowing if we would get back to ABZ that night.
Arriving at AMS hubby went to the transfer desk and was horrified at their attitude which was... we have overbooked you will just have to wait at the gate and see if there is a seat. He asked to speak to a supervisor and was told the same thing. Apparantly hubby was told they do this all the time!!
The long shot was, we did get back to ABZ that night but did not know until 15 mins before the flight left. What I couldn't understand was here was us trying to check in for this flight at noon, some 8 hours ealier and upon speaking to people at the gate, they had only just checked in. I really just could not understand KLM's couldn't care less attitude.
I would definitely keep on at them and ask for an explanation.
Good luck