Ever heard of a LAN? You don't need internet access for every single machine.
Same goes for electronic medical records. There are people who assign ICD-10 codes (insurance billing codes) to patient encounters. Often this is a second job for them and they work remote and typically at odd hours.
A modern hospital cannot operate without internet access. Even a medical practice with a single doctor needs it these days so they can file insurance claims, access medical records from referred patients and all the other myriad reasons we use the internet today.
This stuff isn't impossible to solve. Rather, the incentives just aren’t there. People would rather build an apparatus for blame-shifting than actually just building a better solution.
If modern medicine is dangerous and fragile because of network connected equipment then that should be fixed even if the way it currently works doesn’t allow it.
If you don't understand why it has to be networked with extremely bad fallback to paper, then I suggest working in healthcare for a bit before pontificating on how everything should just go back to the stone age.
The question is not whether or not hospitals need internet at all or to go back into printing things in paper or whatever nobody ever said. The question is whether everything in the hospital should be connected to the internet. Again the example used was simple. Having the computer processing and exporting the data from an MRI machine connected online in order to transfer the data, vs using a separate computer to transfer the data and the first computer is offline. This is how we are supposed to transfer similar data at my work for security reasons. I am not sure why it cannot happen in there. If you cannot transfer data through that computer, there could be an emergency backup plan. But you need to solve only the transfering data part. Not everything.