Sax, it is covered by insurance in Russia too. You overlooked the fact  that Russian companies (employers)are under obligation to  regularly pay to Compulsory Health Insuranse Fund  tax on salary (today it is about 5,1 % of total salary amount which employers pay to employees).

There is nothing for free ( only chees in mousetrap)/

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In Brazil, as many other things provided by state, is free. But not works well as supposed to.

There's a service in Big cities called (SAMU - URGENT MEDICAL SERVICE).

In this service the ambulance has several paramedics and they assist to any emergency call. Inclusive traffic accidents or accidents in general.

In small cities the fireman or city employees has the function to make the first assistance.

Since the state sometimes is slow and maybe you will not get the assistance that you need, you can pay a insurance that covers this service. Although this kind of covert is really expensive.