DL sends necessary data to KL who does all checkin and departure handling. After the flight is departed and closed out, KL sends DL back a file of the passengers boarded etc. KL controls the standby list.

For my recent AMS-BOS flight, I checked in online the evening before and ended up being routed to the KL checkin site and checked in there. As you did, I had to give some further information. Perhaps all information KL wants is not included in the upload of passenger data sent by DL. In the end I had a KL boarding pass and all went smoothly.