Technically they do, on their image. This does not preclude you making your own copy off the same original, public domain census. Quite likely it also does not preclude your transcribing the information as text, since your result in that case could not in any way be distinguished from the result if you had used the original.
An example of where a copyright could be construed over such material would be a book where the 5 or 6 pages leading up to "page 68" and the 5 or 6 pages following were an exact reproduction of the original work prepared by a different author.
My copyright might not be very good concerning certain things, but all it has to do is be better than your copyright to prevail.
That's a case where neither party has any sort of claim to the intellectual property rights involved and is asserting a copyright out of spite.
I would like to see a two-tier "restoration copyright" recognized in law. The first tier would be for much shorter duration than conventional copyright (e.g. three to five years) but would apply to direct reproductions of the original materials. Such a copyright would encourage people who have rare material to publicize it in unaltered form, something for which there is today little incentive.
The second tier would apply to material which is based on previously-published work, but which involves substantial editorial or technical adjustment [e.g. restoring an old movie, using computers to reconstruct portions of frames which are not in usable condition]. The term of this would be much longer--perhaps equal to normal copyright--but with a twist: all source materials used in the restoration would be subject to the first-tier copyright structure, and after the the first-tier copyright term on those materials had expired the publisher of the restoration would have to either make good copies of such materials to anyone who paid a certain statutory price structure, or supply such materials to a recognized repository that could do so. The price structure I'd have in mind would be pretty steep [e.g. $250 for two hours of movie filmed to VHS or DVD; $5,000/hour for 35mm film] but since the material thus acquired would be royalty-free, redistributors would probably not find such prices unaffordable].