Well....not that I necessarily agree, but:
1. States fund/employ/regulate doctors and other heath care staff
2. Until recently, permission was not needed for hospital staff for to take and store organs.
3. Thus, the "state" vis-a-vi hospital staff, could take possession of portions of (if not the entire) bodies of those who had died in hospitals or who's bodies ended up at the hospitals after death.
4. Thus, the "state" had rights to or ownership over the bodies of the deceased.