After many back and forth between Egencia (Expedia Corporate Travel) and Hilton, here is the answer we got from Egencia:

"I just got off the phone with Hilton and got some confirmation around the Hilton Honors programs. It seems there was some miscommunication on this. Your travelers should absolutely receive their loyalty points when booking a published rate with Hilton. They will not if they book an 'Expedia Special Rate,' which is where I believe the confusion is coming from on Hilton's end. But published rates do offer points. I think they were confused because Expedia.com does not offer these types of rates so they are conditioned to push back on this when they see the Expedia name"

So we get the points as long as we do not book an "'Expedia Special Rate".