If it's the case of needing to transfer patient data, say for blood type, couldn't a doctor just call another hospital (by phone) for the patients emergency records and perform the operation?
It isn't just blood type, it is the full medical history.
One of the problems is manufacturer support... They do remote support these days and access the devices and applications over the Internet. No Internet, no support when something doesn't work.
I know the admin at a manufacturing facility, they have an old cutting machine that is bound to software running under XP - it won't install or run on Windows Vista, 7, 8 or 10. To upgrade the software to Windows 10, they'd need a new machine. The old one works fine, reliably and does what is needed of it, so why throw it away and replace it with a new machine costing 7 figures, when it is just the software that doesn't work on newer versions of Windows?
They have isolated it and they do force the manufacturer to do remote support. The first question is the TeamViewer ID, the support are told the device is offline. They say to put it online. They are told, provide software for Windows 10 and we'll put it online. Until that happens, you will remote-control the machine operator with verbal instructions.
That might work for a single manufacturing machine, but a whole hospital full of "machines that go bing" is another matter, unfortunately.
Then there is patient data transfer. The Krankenkassen (health insurance companies) hold the patient data and they collect the billing information from the hospital systems. This should be over a secure Telematik system, but that is still running over the Internet, albeit in a secure tunnel.
That individual monitors, and whole operation rooms are online is a different matter, they should certainly be isolated, whether standalone or an internal isolated network. And there should be disaster recovery scenarios to allow them to keep working if the systems go down. But re-directing patients that are en-route to other hospitals, if there are problems, is SOP - and according to local news, the woman was en-route to the hospital and her ambulance diverted, because the ER was offline and couldn't accept new patients, she wasn't transferred.