Yeah, the issue is not having the ice to train, there are a lot of ice rinks in Moscow. The issue is that Russian Figure Skating Feds don't like when skaters competing for other countries, training on the same rinks and at the same time as Russian skaters. Russian coaches are direct states employees. Sport facilities (and stuff) are built and supported by RSF's money. Several Russian athletes are sponsored by private Russian money as well.
I certainly sure a Russian figure skating fans and even officials would not mind when someone like Carolina Kostner training on the same ice with the same coaches as other Russian athletes, as long she is paying for it. The press and overly patriotic journalists are the main problem. Let's say if Carolina can skate clean and as usual beautifully, and would get first place, it would not be a big tragedy in Russia as long it's a fair play "sport" result.
However their internal sport politics and competition among Russian coaches or sport clubs might play a bigger role. Someone can whisper to Russian press something let's say about Carolina training on the same hours as Russians (hours paid by Russian state & fed) - the next day there would be few hooray-patriotic articles in the newspapers.. It is well-known that Russians coaches always were training foreign athletes, most of the time on the same rinks and the same time with other Russians athletes, as long they are doing it quietly Russians officials did not really mind of coaches making some more money on a side. They are free people, they can have private students as well as Russian skaters funded by the state. Politicians don't really care too. Until some journalist would not make it public and create the overly patriotic noise out of it, to make Russian public outraged for the specific purpose to influence internal political game within skating federation.
I think Russian FS fans don't really mind, as long as their favorites are not totally neglected or loosing competitions all the time miserably. So, before Olympics Russian coaches, officials and even TAT probably decided not to risk it with public opinion. But they were free to train other foreign athletes afterhours on any other available rink across Moscow. The Feds might made few hints to coaches about Sochi being special, because it's home Olympics after all and private tutoring won't be tolerated that year. Besides coaches are the same federal employees paid by state funds (and Russian taxpayers) and bonded by corporative contract. Conflict of interests, moral issues and all that jazz.

They like their jobs, so decided not to risk it before Sochi.
It's financial issues too, basically Russian officials don't want to be seen publicly as sponsoring and financing non-Russian athletes. No one has a beef with Vasiljevs training with Yulia on the same time and rink under Urmanov wing. Even though the rink they train is a part of 'Sirius' - school for talented kids (not only athletes, also arts, science, literature and etc) - is sponsored by Russian feds. But if someone (like journalists) would make a big deal out of Vasilijevs winning too much, there would be the whole different story...