I'm using skymiles to book a skyteam award ticket to FCO in the summer. Of course, availability is terrible, and the DL representatives cannot find anything. However, I've found a few options using vinnmann's great post. To do this, I used the NW and CO websites to find connections (I couldn't make any sense of KVS).
While doing this, I found a discrepancy between DL representatives for KLM flights, and I was curious if anyone here had run across this, or solved this problem in the past. KLM has a few daily flights directly from AMS to FCO, but DL reps can only see up to flight KLM 1601, and nothing later in the day. There are two others (1607 & 1609) with much better availability according to the NW website. On two occasions (of many), the DL rep has been able to make a phone call and get availability for the 1607 and 1609 flights. Other DL reps insist that there is no availability, and that these flights are not even offered for skymiles since they don't show up on their searches. When I tell them about my previous successful experience, they respond that it must have been a mistake. When I tell them about the availability I've found on the NW site they tell me that not all skysaver class seats are available to all skyteam members, suggesting that NW has access to these flights, while DL does not.
So, my question is, is it possible for some skyteam members to have better access to other members inventory than the rest? If not, how do I explain this to the DL reps? I have only had this problem with KLM flights found on the NW website. I assumed that if a non-NW flight showed up on the NW website, it was available to the entire skyteam, as vinnmann suggested. Thanks for any clarification!

Shawn