Sinking friendly ships disguised as enemies is one thing, hospital ships are something else entirely.
Germany took this very seriously when others didn't: There were confirmed attacks on clearly marked hospital ships by British, American and Japanese forces.
Germany complained rather loudly after the sinking of the hospital ship Tübingen, and Dönitz also reacted very strongly when told that Italy was in the habit of misusing hospital ships for military purposes.
All in all, I think being shot at dawn is entirely realistic here.
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