I have certifications in data privacy.
The idea that data is "property" or that it is "owned" by anyone is not codified in law. And as an analogy for how GDPR works, I think it's more harmful than helpful. I see GDPR as rejecting the idea that data has an owner, more than anything.
GDPR says that the data subject has rights to data about them. If you want to put a label on it, I would say that legally they are a stakeholder in their own data. One stakeholder of several. Not necessarily the most prominent one. GDPR gives you a seat at the table, but it doesn't actually put you in charge, the way that "ownership" implies.
The company that collects & processes the data is still the one making decisions like: What data is being collected? What is it used for? What is the Legal Basis for data collection? What Processors will the data be sent to? What countries will the data be processed in? They have a lot of leeway in how they answer these questions and still be compliant with GDPR.
So for that reason, my view is that GDPR says there are multiple stakeholders will different rights to how the data is handled. Which if anything is a rejection of the idea that the data has an owner. Certainly you have rights to the data, but some of those rights have limits, and the Controller still has right as well.