No, it does not. If you pay taxes here, you have to have health insurance. For a permanent employee, this is about 14% of your salary. All in, I pay about a third of my income in tax (which includes health insurance).
but the 14% are split between yourself and your employer. only your part is taken directly off your paycheck.
Is that a cross-Europe thing then? My fiancée is Swedish but living in the UK with me; as far as I know she doesn’t pay any extra tax or have extra health-insurance.