KLM is responsible for the bags. I'm not even sure that SkyTeam has much to do with this and think it defaults to IATA rules.

Sorry that this happened.

Not that it helps now, but for those planning later, it should be noted that European airlines mishandle bags at a much higher rate than the worldwide average and triple the rate of the US. Not sure what that means the consumer should do, other than pack some extra underwear.