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Nazi Germany's Euthanasia murders would probably not have been possible without a reasonable amount of collaboration from the medical sector. Not sure if that is relevant to your question, however.
I think your lumping together of authoritarianism and corruption is not particularly useful. The two sometimes come hand in hand and sometimes not. E.g. I would claim that in East Germany (which was quite authoritarian but not very corrupt), fire brigades and emergency services were reasonably similar to what it is now. The equipment was worse and the civil defense forces were somewhat more geared towards military conflict than the THW is. But fire brigades and ambulances generally did what fire brigades and ambulances are supposed to do.
As far as I have heard from countries with greater problems re. corruption, the health sector often is quite corrupt, but that generally applies more to hospitals and doctors and not so much to emergency services. It is mainly a matter of opportunity and social acceptance. Nobody will complain to authorities if you give the doctor some money for a day of sick leave, or for moving you up a few places on a waiting list. But if the fire brigade refuses to put out a fire if it does not get a bakshish first, then some people will get really upset, report it to the media etc.
P.S. police in authoritarian countries would still claim that they are protecting order and thereby protecting citizens.