I just tried to replicate the OT's experience. I even went to klm.us, then clicked Multiple Destinations and inserted a trip MIL-ORD-CPH. As soon as flights were displayed, the website clearly showed this message:
"Because you have chosen to depart from Italy, all prices will now be in EUR. Our KLM Ticket Office in Italy will gladly handle your payment and issue your ticket. Please also see our Currency Converter at the bottom of this page."
I think this is quite transparent; to me this is a clear indication that the rules of an Italy POS apply and the US website/customer service/KLM agents etc have nothing to do with it in this case.