What guarantees that the doctor is willing to help, especially if they are hired in a public system?
Nothing
In the end, the doctor with the perfect resume could end up killing you because for whatever reason.
However, you have this issue with any group of humans. How do you know your fellow teammate in sports will not choke you? How do you know your fellow soldier will not shoot you?
There are systems that prevent doctors from abusing their options:
- Law
Obviously, killing someone will lead to persecution and possible conviction with different penalties depending on the legislation
- Employment.
If a doctor messes up and it's solely their fault, chances are they are going to get fired and have a hard time (as in impossible in Germany, for example) to get employed again and will usually have their certificate revoked in the meantime.
- Reputation.
Doctor have to make money. They have either themselves or a family to feed. If they do you harm, they are going to lose reputation and make less money
- Helper Syndrome.
Those who care not that much about money usually become doctors because of the helper syndrome. They want to help other people. (That's why I'm answering your question here, as an example). They would not do you any harm because it goes against their ideals, and against the reason for why they became doctors in the first place.
What you can do
Doctors are humans (apart from the people who work 80 hour weeks and 3 24-hour shifts in a week, which I suppose are either vampires or zombies).
You can rely on common sense which will usually tell you whether you should trust that person. If you don't trust your doctor, change them. Trust is very important in a doctor-patient relationship.
If you feel bad or have fears, either confront the doctor directly, talk to someone else or make an appointment with a psychologist.
In the end
Doctors might be more scary because they know more about you and your body/health, but in the end the taxi driver around the corner could also kill you.
It's just a matter of reasonability. The health system has options implemented to make abuse more difficult, but it's possible.
Trust in your ability to judge other people and use it.