That is not accurate.
It applies to European carriers at all times, but it also applies to non-European carriers on trips that depart from the EU. The fact that OP had a leg on both KL and DL on their ticket (and that KL was the original cause of the delay) is not relevant - when a EU261-qualified delay happens (on a single ticket with multiple carriers), you file with the operating carrier that got you to your final destination (DL may send the bill to KL for this one). If it had been a DL codeshare on a KL operated AMS-DTW, KL would have been the target to file with.