You are correct in the fact that the kidney's are one route of clearance for small agents that are injected. However, these are typically small molecule agents or particles on the lower size range at a couple nms in diameter. To reference a highly sited scientific article from Chemical Rev (Chem. Rev. 2010, 110, 2921–2959), "At 8 nm, observations have been made that hepatic uptake begins to dominate clearance routes, and by 10-12 nm the reticuloendothelial excretion route becomes the dominant route for clearance."

These nanodiamonds range in size from 15-100nm, so the kidneys will not be their primary route of clearance. It is also crucial to note that with any nanoparticle development, coating is a major factor in its biodistribution behavior. Coatings can and have been designed in more recent work regarding nanomedicine that minimize various biodistribution issues.