"Any tissue sample that is given in a hospital or any medical facility, once it's given, is no longer your property," Lorey explained. "You can agree with that or disagree with that, but it happens to be the law." If true this is incredibly depressing. I don't know very much about patient privacy laws but have some follow up questions for those more knowledgeable: 1) I assume this quote refers to California state law…
The fact is, for some things (like tissue samples with DNA), it's important to recognize that non-owners can have a stake in is done with something. The originator of a tissue sample cannot entirely severe their connection with that tissue, and that means that the new owner shouldn't be able to claim unrestricted ownership. The legality should recognize ways in which the non-owner can be affected by the owner's interactions with the sample.
(Aside: GDPR works by essentially doing the same thing with data. The "Rights of the Data Subject" stipulate that a non-owner of the data is still a stakeholder in that data.)
[1] Although, ironically, that actually makes property law well-suited to addressing the situation. In Common Law, the idea of 'ownership' is understood as 'a bundle of rights,' which can be un-bundled. A framework for addressing the situation is to enumerate separable rights for tissue samples, and stipulate different rules for delegating those rights.