I just booked another flight using the IAP, and I actually had a similar experience to what you mention where at first glance it was more expensive with IAP.
I was looking at travel from SEA to FCO and there were a bunch of options showing up with airlines that are part of IAP (I was seeing LHR, BA and DA) and all averaging around 3,2xx round trip in Business. I called the platinum travel line and asked about flights on the dates I was looking for and they said the cheapest flight was 3,3xx, so more expensive than what I was finding online. HOWEVER, when I asked them for a specific itinerary by giving them the exact Lufthansa flight numbers that I wanted, then they were able to find it for 2,8xx. Including the $39 booking fee I ended up saving around $300 which is not terrible, specially considering that the total ticket price is pretty good for a round trip business class flight. So now I know that I can't just ask them for prices, I need to have a specific routing in mind and then I get a better price.