Not necessary true. Russian media is just doing their job - they reporting. The problem is other people - some retired skaters, coaches, experts, commentators, journalists and fans - some of them support Zhenya, some not so much. They are expressing their thoughts in the press. And it's journalists' duty to report and to publish all that. They can't just censor every piece that is somewhat negative or analytical about recent Zhenya's performances. Zhenya is just too young and inexperience to handle her PR more in her favor.
Well, for just instance there is influential Moscow local channel - Moscow-24. This is basically Moscow city government PR pet project. It is very hypsterish and full of young journalists. Although they are overly enthusiastic when the major of Moscow is opening a newly reconstructed park, or riding a bicycle to work, or shaking hands of subway construction workers, but the rest of 90% of time they do whatever they want. They reporting on all events in Moscow and shooting some seriously cool documentaries about the city. They routinely make interviews with a lot of athletes who train in Moscow, they also interviewed Zhenya a lot in the past. They were reporting on all her victories, they were meeting her in the airport after WC, GP and Euros. They ran a flashmob just 2 days ago with a hashtag of support and promised to show all the best videos and pictures for Zhenya by fans from social networks on their TV:
https://www.youtube.com/watch?v=0sLkGDXgjrw This TV channel is quite popular among Moscow youth, hipsters and alike.