Is it true that international students can study for free at Russian universities?

Yes, it's true. International students can try any of several ways to qualify for free tuition. For example, they can take part in Olympiads arranged by Russian universities; the winners can be admitted to the university without taking entrance examinations and are entitled to free tuition or various admission preferences. Foreign nationals can also apply for Russian government scholarship. Some groups of foreigners can study for free on equal terms with Russians. To learn more, please see A Step-by-Step Guide to Applying and Academic Competitions for International Applicants sections. 

Please note that in all the above cases, foreigners enjoy free tuition, yet they will need to cover the travel costs to Russia, medical insurance, accommodation and everyday expenses with their own money.