I'm using the REST API with two Sharepoint installations (one using Sharepoint Online, the second using Sharepoint Server).
When I'm using Sharepoint Online, everything is fine. When I'm using Sharepoint Server, all the Create/Update/Delete operations are declined, answering with the same error message I would have if I hadn't sent the valid form digest value in the header (X-RequestDigest).
I checked the headers of my requests, and I was able to make sure that the X-RequestDigest value was both present and valid.
So I've been wondering... it's nowhere in the documentation, but is there perhaps something to do on a Sharepoint Server to enable Create/Update/Delete operations when using the REST API ?