IIRC, Obama's attorneys filed for a protective order from Berg's discovery requests. I don;t know how it played out, but discovery requests don't come from the judge, they come from the other side. Legal wrangling as to what discovery requests should be granted occurs in most civil lawsuits. Until and unless the judge rules on the various legal motions that fly around during the discovery process, a discovery request from one party to the other has no legal force.
And even if theObama defense team refused to hand over some documentation even after a court order, you wouldn't likely see the DOJ getting involved. The most likely worst result would be the entering of a defualt judgment against them.
I believe you are correct.