> "Surely connected devices could use one centrally calculated timesource?"
... like NTP?
Sorry, but I'm not sure what point you are trying to make here. Anything with a computer, even a microcontroller, and basic network connectivity can use NTP, it is an extremely simple protocol.
Anything that doesn't connect to a network could be kept in sync via a wireless pulse/tick, though then you have security issues unless you cryptographically sign the clock signal. Though I'm not sure why anybody would try and screw up a clock signal like that other than general asshattedness.
That aside, I'm unsure why they are using local time for logging data anyhow. If the folks managing the hospital were rational, shouldn't there be a regulation to use GMT and 24-hour clock? My home town is right on the Eastern/Central timezone split, and I know it causes all kinds of problems in day-to-day life. I just hate that kind of ambiguity.