Russia is already in process of providing Snowden with the necessary documents etc for his stay, it's just a matter of a lot of red tape there.
And yes, Russia has leakers and political refugees, too. And a lot of them go to US or other free(er) countries, and Russia generally doesn't raise much fuss about it, at least not to the point of threatening sanctions.
Heck, Europe and US have a bunch of guys from Chechen government-in-exile, and some other people who participated in either or both Chechen wars, whom the Russian government considers terrorist - and they have far more grounds for that (we're talking about guys who actually killed people).
The only strange part of that story is that US is whining so much about Snowden. It all sounds very personal, as if he has a private video of a Congress group masturbation stashed away or something.