Wait a sec!
Wasn't the primary reason for why he suffers from "adamantium poisoning", because his healing factor had to balance out that he could no longer recieve new blood cells via his bone marrow, because the metal sealed them off completely?
Essentialy without his healing factor to artifical regenerate them, his body would beginn to break down from no longer being able to seal off wounds (platlettes), transfer enough oxygen and nutrients (red blood cells) or fight disease, tumors or parasites (white blood cells) eventualy.
Hence why people with only partial adamantium implants or bone coating (like Bullseye with his spine) don't suffer the same effect.