So... since when does russia care about the US? They sure didnt last week. So here's what I think happened. The US talked with Russia and told him to hand Snowden over. Russia refused, citing they would lose face. They also made it clear there were things they wanted from the US. They were willing to deny him asylum and the US said they were most concerned about the other information Snowden has available to leak. An agreement was reached. Russia was given something they wanted and in exchange they said they would offer him asylum on condition he turn over all data. That'd be my guess. Its even possible that, if Snowden foolishly agrees, Russia may trump up a criminal charge 3 months from now and say they are revoking asylum and shipping him to the US (secretly in exchange for something else they want.) This is the great game nations play with one another. They have done so for eons.
U.S., allies conduct 1 air strike in Syria and 11 in Iraq against ISIS militants (Reuters)
from the article: Putin: If Snowden wants to stay in Russia, he must stop harming U.S.