OFICIALLY it’s true. Medicine and education have been free of charge since the Soviet times. As for medicine, you really don’t pay for a visit to doctor but all the medications you have to buy on your own, and they are really expensive. Education can be free only for the Russian citizens and only in case they study “on budget”. In some universities there are a few vacant places for students which are paid by the government. These places are called “budget places”. They are usually supposed for especially talented and prominent students.
I heard that people in Lybia had free medicine and education too. Before the revolution, though. I don’t know about now.
Anyway I’m almost sure that Russia is not the only country to have those services free.