More thna a few people with the D600 reported the issue didn't stop and not even significantly reduced after many more shots than 3,000. I've seen this problem on several other models, including other Nikons and Canons, but the D600 has a significantly more of it and a lot more of them have this issue it seems.
Re oil or dust, Nikon just says users report an issue but they don't actually say what it is. I mean, they write dust, but obviously they write it in the vaguest way possible. I'm wondering if someone will be determined enough to try to test it at a lab to find out.