There is nothing being returned here, since the hospital has not lost access to the data, and the threat is that private data will be published.
This is just blackmail.
What is it then, if you don't have the legal right to the data?
It's not like we need the law to explicitly allow types of access. Anything not explicitly disallowed is allowed without a special name.
"Stealing" happens when the original owner is deprived of the thing.
Both "hacking" and stealing are illegal in most countries, but they're still completely different actions: one is taking a physical object from someone, the other is sending and receiving electrical pulses trough a wire.
You wouldn't call stealing and killing by the same word, either, even though both are illegal.
Seriously. Theft requires the property owner be denied their property.
What happened is someone made a copy they were not supposed to.
Textbook infringement.
What makes "stealing" particularly bad is that the rightful owner no longer has possession of their property. That's not necessarily the case with data.
In digital, information wants to be free and many kinds of resources are effectively unlimited. There is no material scarcity. Therefore, theft, in the digital world, can't be the same as it is in our analog world.
To be fair, this also applies to copyright and peoples' foolish notion that they can protect data without a great amount of preventing otherwise normal "physiological" processes. (Ironically, rather than having a wake-up moment where people realize their folly, we've institutionalized these resource-scarcity regimes into resource-abundant versions in the digital world)
To summarize, info wants to be free, and since theft requires extra effort to deprive someone of what you stole, does that definition of theft really apply here? Or does it need to change given the context? And, as a secondary point, people like to think they can protect data but their brains are stuck in our analog, resource-scarce world