My org does a ton of direct billings with all sorts of hotels. A lot of them may be small groups or individuals; I think those instances they may be eligible rates. However, the large majority of rooms we book (and direct bill) are larger groups where there's a block of rooms and an event contract signed (with and without meeting space/catering). Those are never eligible rates and no qualifying credits are earned. The points go to whoever is named as the points recipient in the contract.
Some hotels will be sticklers and deny benefits according to the policies. But I've been fortunate to have received elite benefits at a couple of our regular hotels where events are booked and direct billed.