Was the KLM constantly in Controlled Airspace, or was it transferring between civil & military ATC ?
If it was working the military at any point it may well have had the code changed.
Otherwise, the ORCAM code allocation ought to provide a discrete code for the a/c. But, with so many a/c flying about & the shortage of Mode A codes (4096 available), it can happen that duplication of codes occurs & someone has to change the squawk to avoid confusion.
I would say that the only time that you can tell which Agency (ATC) is controlling the a/c from the code is when the code is first allocated & the a/c is still within its area. Even in this case, it may be impossible to decipher which frequency that the a/c is working eg. The one that issued the squawk, or the one that it has since been transferred to (without a change of squawk).