It would be beyond stupid to take DNA samples from the exposed surface of the skulls. SURELY the DNA samples would be taken from bone matter below the surface. No scientist in his right mind would use a surface sample from a 2000 year old specimen. There is no way.
Bone is porous. The simple act of handling the skulls with bare hands would introduce DNA from the handlers, which can easily penetrate at least a few mm into the bone.
If I were doing a DNA extraction from these skulls, I would be choosing a section of bone that is deep inside, as far from surface contaminants as possible. For example, I might choose a sample from inside the sinuses. And then I would run a slew of controls to rule out the possibility that modern DNA is contaminating the results.
Unless you have actually worked with DNA and tried to analyze it, I do not think you can fully appreciate the problem of contamination of samples. Even airborne DNA can contaminate your samples. Avoiding DNA contamination is a very exacting process.
This subject is right up my lane of expertise. My PhD is in biochemistry (the study of proteins and metabolism) and molecular biology (the study of nucleic acids).